Approach For Stability Analysis Research Articles

Unified Approach for Robust Stability Analysis of Buck Converters with Discrete-Time Sliding Mode Control

This paper proposes a novel discrete-time sliding mode (DTSM) control approach to address the robust stability problem of buck converters with multiple disturbances. The contributions lie in the “unified” modelling and controller design. In modelling, all the possible model uncertainties and external disturbances are considered and further classified into two cases. It can also be extended to the situations with individual/several disturbances. While for the controller design, differing from the traditional DTSM based on the nominal model, the disturbances are directly introduced in the process, giving the robust stability condition and four new regulation subranges. It is suitable for both nominal and perturbed systems. Finally, the influences of the sampling time and disturbances on the control performance are investigated. Simulations and experiments confirm the benefits of the unified approach with greater accuracy and wider applications.

Stability and Anti-Chaos Control of Discrete Quadratic Maps

A dynamical system describes the consequence of the current state of an event or particle in future. The models expressed by functions in the dynamical systems are more often deterministic, but these functions might also be stochastic in some cases. The prediction of the system's behavior in future is studied with the analytical solution of the implicit relations (Differential, Difference equations) and simulations. A discrete-time first order system of equations with quadratic nonlinearity is considered for study in this work. Classical approach of stability analysis using Jury's condition is employed to analyze the system's stability. The chaotic nature of the dynamical system is illustrated by the bifurcation theory. The enhancement of chaos is performed using Cosine Chaotification Technique (CCT).
 Simulations are carried out for different parameter values.

A Probabilistic Approach for Contact Stability and Contact Safety Analysis of Robotic Intracardiac Catheter.

The disturbances caused by the blood flow and tissue surface motions are major concerns during the motion planning of an intracardiac robotic catheter. Maintaining a stable and safe contact on the desired ablation point is essential for achieving effective lesions during the ablation procedure. In this paper, a probabilistic formulation of the contact stability and the contact safety for intravascular cardiac catheters under the blood flow and surface motion disturbances is presented. Probabilistic contact stability and contact safety metrics, employing a sample-based representation of the blood flow velocity distribution and the heart motion trajectory, are introduced. Finally, the contact stability and safety for an magnetic resonance imaging-actuated robotic catheter under main pulmonary artery blood flow disturbances and left ventricle surface motion disturbances are analyzed in simulation as example scenarios.

Numerical approach for bifurcation and orbital stability analysis of periodic motions of a 2-DOF autonomous Hamiltonian system

In Spaceflight Dynamics it is often necessary to obtain periodic motions of conservative mechanical systems and analyze their stability and bifurcation. These conservative systems can be described using Hamiltonian equations. We consider bifurcation and orbital stability problem for periodic motions of a 2-DOF autonomous Hamiltonian system. Since it is not possible to obtain analytical solutions to the aforementioned problem for all admissible values of its parameters a two-step numerical approach is proposed. On the first step the so-called base solutions are obtained analytically for particular values of problem’s parameters. The base solutions are then continued to the borders of their existence domains using a numerical algorithm. In course of computation bifurcation points are identified and orbital stability is studied. On the second step new base solutions are identified in the neighborhood of bifurcation points and the continuation process is repeated. Finally, orbital stability and bifurcation diagrams of the resulting families of periodic motions are constructed. Poincare sections are also computed in the neighborhoods of bifurcation points to verify the results. To illustrate this approach, we computed the bifurcation and orbital stability diagrams for families of short-periodic motions originating from Regular precessions of a dynamically-symmetric satellite.

A review on transient stability of land-sea networked fishery microgrids

The islands and offshore fish farming platforms in the deep sea can form a land-sea networked fishery microgrids to realize the complementary supply of energy. The fishery microgrid contains a high proportion of renewable energy sources such as wind, solar and waves, and mixed AC and DC loads such as feed machine, energy storage, and fishery robot. Due to the harsh operating environment, the possibility of equipment damage increases, and the requirements for system stability are higher. In this paper, firstly, the definition of transient stability of land-sea networked fishery microgrids is given. Then, the key features of the fishery microgrid is introduced, and the influence of the microsource interface type, control strategy, current limiting mechanism and load characteristics on the transient stability is expounded. The definition of power Angle of fishery microgrid and the characterization of instability system are given. Next, the research trends of transient stability are sorted out, evaluated and discussed from two aspects: approaches of transient stability analysis and methods to improve transient stability. Finally, the key issues that need to be solved urgently in the research on the transient stability of the land-sea networked fishery microgrids are summarized, and the relevant research directions are prospected.

Energy Function Based Transient Stability Analysis of Power System Integrated with DFIG

The access of large-scale wind power seriously threatens the safe and stable operation of the power system. In this paper, a novel energy function based transient stability analysis approach is proposed for the power system integrated with Double Fed Induction Generator (DFIG). First, the network structure-preserving model of power system integrated with DFIG is established, where generators adopt 3th order electromechanical model, and its energy function is deduced. Next, the energy function of post-fault system is approximately calculated by trapezoidal integral path, and energy function based transient stability criteria are put forward to access the stability of the post-fault system. Finally, the New England-39 bus system integrated with DFIG is used as test system to investigate the validity of the proposed approach.

Membership-Function-Dependent Control Design and Stability Analysis of Interval Type-2 Sampled-Data Fuzzy-Model-Based Control System

This article investigates the design and stability analysis of the interval type-2 (IT2) sampled-data (SD) fuzzy-model-based (FMB) control system with the optimal guaranteed cost performance. An IT2 Takagi–Sugeno (T-S) fuzzy model is applied to describe the dynamics of the nonlinear systems where the parameter uncertainties are captured by the lower and upper membership functions. To conduct the stability analysis for the SD FMB control system, a looped-functional approach taking the advantage of the information about the sampling periods is employed. Because of the SD control strategy, the state will be sampled at each sampling instant and the control signal generated by the IT2SD fuzzy controller will be kept by the zero-order holder during the sampling period, which will result in mismatched membership grades between IT2 T-S fuzzy model and IT2SD fuzzy controller that leads to the complexity in carrying out stability analysis. Thanks to the imperfect premise matching concept, which allows the difference on the number of rules and the premise membership functions between model and controller, the design of the IT2SD fuzzy controller can be more flexible. To further relax the stability conditions and minimize the upper bound of the guaranteed cost index, the membership-function-dependent stability analysis approach which can make use of the features of the IT2 membership functions is adopted. The performance of the control system can also be adjusted through the choice of the weighting matrices in the cost function. The stability conditions building on the Lyapunov stability theory and the performance conditions building on the concept of the guaranteed cost control in the shape of linear matrix inequalities are established to assure the system stability and acquire the optimal guaranteed cost performance. The proposed IT2SDFMB control design is tested on the inverted pendulum system and the simulation results verify the effectiveness of the proposed approach.

Design of borehole deployments for slope stability analysis based on a probabilistic approach

This study proposes a cross-correlation map-based borehole deployment approach for two-dimensional probabilistic slope stability analysis. This approach designs the layout of the proper number of boreholes based on the cross-correlation between the factor of safety and spatially variable soil strength every part of a slope. Numerically synthesized, undrained slopes are investigated as examples to illustrate the effectiveness of the proposed approach. Results demonstrate that the proposed approach is viable, and the cross-correlation maps are the appropriate metric for design slope borehole deployment. Using the cross-correlation maps, a small number of boreholes can sufficiently capture the large-scale heterogeneities that are critical to the slope stability. This information can help to identify the slip surface and improve the slope stability analysis. The small-scale heterogeneity, due to its short correlation structure or the residual covariance of the soil property field after conditioning using the borehole data, leads to a small amount of uncertainty in slope stability analysis. This small uncertainty could be vital to the slope stability analysis when the slope stability is close to the limit equilibrium state.

Designing controller parameters of an LPV system via design space exploration

This paper deals with the stabilizability problem of liner parameter varying (LPV) systems. It is assumed that LPV models affinely depend on time-varying uncertain and time-invariant design parameters. The uncertain parameters, their time-derivations, and design parameters belong to polygonal convex spaces. The stabilizability problem of such systems is studied. Extending the stability conditions to stabilizability conditions generally causes nonlinearity issues due to the coupling between the Lyapunov and design variables. To cope with this issue, a design space exploration algorithm (DSEA) is proposed to accurately determine the design parameters with a feasibility performance similar to stability analysis approaches. DSEA removes the undesired parts of the design subspace that cannot stabilize the model. Then, it checks the corner points of the remaining subspaces to find a stabilizing point. This procedure continues until a stabilizing point is found or the whole design subspaces are detected to be undesirable. Three hundred random LPV systems are generated to compare the feasibility performance of DSEA with existing approaches. Also, the proposed approach is used to stabilize the LPV model of a microgrid consisting of several distributed generation units and energy storage systems. The simulation results show the superiority of DSEA over the existing approaches.

Membership Function Derivatives Transformation Approach for Stability Analysis and Stabilization Control of T-S Fuzzy Systems.

In this text, a membership function derivatives (MFDs) extrema-based method is proposed to relax the conservatism both in stability analysis and synthesis problems of Takagi-Sugeno fuzzy systems. By the designed algorithm, the nonpositiveness of the MFDs extrema is conquered. For an open-loop system, based on certain information of the MFs and derivatives, a series of convex stability conditions is derived. Then, an extremum-based construction method is adopted to involve the MF information. For the shape of MFDs, a coordinate transformation algorithm is proposed to involve it in the stability conditions to achieve local stable effects. For a state-feedback control system, conditions guaranteeing the stability and robustness are listed. Finally, simulation examples and comparisons are carried out to clarify the conservatism reduction results of the raised method.

A new anisotropic continuum traffic flow model with anticipation driving behavior

Based on the anticipation driving car-following model, a new macro traffic flow model is established in this paper by considering the relationship between micro and macro variables. Therefore, the evolution law of traffic flow with anticipation driving effect can be studied from macroscopic level. By using approaches of linear stability analysis, the linear stability discriminant condition of the new macro model to keep the traffic flow stable against small disturbance is obtained. Numerical experiments verify that the model can not only simulate the unique shock wave, rarefaction wave mutation and the dynamic propagation process of small disturbance, but also improve the stability of traffic flow by introducing the information of anticipation driving behavior.

Global Stability Analysis of the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics

Devastatingly, in spite of the long standing research works on HIV/AIDS infection and treatment dynamics, reviews of existing models clearly shown that the behavioral attitude to treatment consistency by those screened to become aware and those receiving treatment have not been given the desired attention. Moreso, the inconsistency following avoidable treatment truncation and later resumption of treatment by these classes of infectives, which could lead to colossal drug abuse is also not accorded the much expected consideration. Therefore, in this present study, we sought and formulated a nonlinear 6-Dimensional deterministic mathematical HIV/AIDS dynamic model that accounted for the global stability analysis of the role of antiretroviral therapy abuse for the treatment of HIV/AIDS epidemic. The model is structured upon dynamical interactions between 6-subpopulations and HI-virus under bilinear control functions with constant screening of the susceptible. It is assumed that the rate of resumption of ART upon truncation is less than initial ART truncation following the incorporation of HIV aware infectives not ready to receive ART treatment and HIV aware infectives with truncated treatment protocol The system mathematical well-posedness was investigated and model reproduction number determined for both off- treatment (with value ) and for onset-treatment (with value ). We considered the model for off-treatment and thereafter by incorporating LaSalle’s invariant principle into classical Lyapunov function method, we presented an approach for the global stability analysis of the role of ART abuse in HIV/AIDS treatment. Furthermore, the analysis and results of this paper presented a dynamic methodological application of bilinear control functions and an impeccable understanding of the fundamental mechanism in HIV/AIDS treatment in the presence of ART abuse. Using in-built Runge-Kutta of order of precision 4 in a Mathcad surface, numerical validity of model is conducted to investigate the study theoretical and analytical predictions. Results shows that application of onset-treatment functions with trend of ART abuse yield tremendous reduction in HIV/AIDS infection epidemic following the recovery rate of the susceptible population with value increasing from 0.5 cells/mm³ to 1.203 cells/mm³ within the first months and attained stability of 0.62 cells/mm³ through the time interval of 20- 30 months.

Global stability analysis of the role of multi-therapies and non-pharmaceutical treatment protocols for COVID-19 pandemic.

In this paper, we sought and presented an 8-Dimensional deterministic mathematical COVID-19 dynamic model that accounted for the global stability analysis of the role of dual-bilinear treatment protocols of COVID-19 infection. The model, which is characterized by human-to-human transmission mode was investigated using dual non-pharmaceutical (face-masking and social distancing) and dual pharmaceutical (hydroxylchloroquine and azithromycin) as control functions following the interplay of susceptible population and varying infectious population. First, we investigated the model state-space and then established and computed the system reproduction number for both off-treatment and for onset-treatment . We considered the model for off-treatment and thereafter by incorporating the theory of LaSalle's invariant principle into the classical method of Lyapunov functions, we presented an approach for global stability analysis of COVID-19 dynamics. Numerical verification of system theoretical predictions was computed using in-built Runge-Kutta of order of precision 4 in a Mathcad surface. The set approach produces highly significant results in the main text. For example, while rapid population extinction was observed by the susceptible under off-treatment scenario in the first days, the application of non-pharmaceuticals at early stage of infection proved very effective strategy in curtailing the spread of the virus. Moreso, the implementation of dual pharmacotherapies in conjunction with non-pharmaceuticals yields tremendous rejuvenation of susceptible population () with maximal reduction in the rates of isolation, super spreaders and hospitalization of the infectives. Thus, experimental results of investigation affirm the suitability of proposed model for the control and treatment of the deadly disease provided individuals adheres to treatment protocols.

A robust stochastic stability analysis approach for power system considering wind speed prediction error based on Markov model

This paper proposes a robust stochastic stability analysis approach with partly unknown transition probability by considering the wind speed prediction error in power system. Firstly, taking this prediction error into account, based on Markov modeling theory, the stochastic dynamic model of wind power system with uncertain transition probability is developed. Secondly, according to the stochastic stability theory of Markov jump system, the transition probability of wind power system mode is divided into three cases: fully known, only known upper and lower bounds, and completely unknown. Then, by using linear matrix inequality (LMI) technology, a robust stochastic stability criterion with disturbance attenuation is obtained. Finally, test results show that the proposed analysis approach does not need to obtain the trajectory of the actual system operation parameters, and has the advantages of high computational efficiency.

Consensus stability in multi-agent systems with periodically switched communication topology using Floquet theory

The stability of consensus in linear and nonlinear multi-agent systems with periodically switched communication topology is studied using Floquet theory. The proposed strategy is illustrated for the cases of consensus in linear single-integrator, higher-order integrator, and leader-follower consensus. In addition, the application of Floquet theory in analyzing special cases such as switched systems with joint connectivity, unstable subsystems, and nonlinear systems, including the use of feedback linearization and local linearization in the Kuramoto model, is also studied. By utilizing Floquet theory for multi-agent systems with periodically switched communication topologies, one can simultaneously evaluate the effects of each subsystem’s convergence rate and dwell time on overall behavior. Numerical simulation results are presented to demonstrate the efficacy of the proposed approach in stability analysis of all these cases.

On the spurious entropy generation encountered in hybrid linear thermoacoustic models

This work demonstrates that a hybrid approach for linear thermoacoustic stability analysis that combines the Linearized Navier–Stokes Equations (LNSE) with a global Flame Transfer Function (FTF), generates spurious entropy waves when used to model acoustically forced premixed flames. The inability of the global FTF to account for the effects of flame movement is identified as the root cause of this unphysical behavior. Utilization of a local FTF, which resolves unsteady heat release on scales comparable to the reaction zone of the flame, suppresses the spurious entropy perturbations. This affirms that fine-grained resolution of the spatio-temporal distribution of heat release rate fluctuations in the combustion zone is required to model the movement of the flame front, even for acoustically and convectively compact flames. As an alternative to hybrid models, a Linearized Reactive Flow (LRF) approach is employed, which extends the LNSE by the linearized species transport equations as well as the reaction mechanism. Such a monolithic approach inherently accounts for the locally resolved flame dynamics, including the movement of the flame front, and does not require an external model for the flame-flow interaction. Thus the LRF eliminates the need for the cumbersome identification of a local FTF. Two configurations of lean premixed methane-air flames, i.e. a freely propagating 1D flame and a 2D flame anchored in a duct, are considered for validation. All results obtained with linearized modeling approaches and conclusions deduced thereof are validated against high resolution CFD results with excellent quantitative accuracy.

Hysteresis and linear stability analysis on multiple steady-state solutions to the Poisson-Nernst-Planck equations with steric interactions.

In this work, we numerically study linear stability of multiple steady-state solutions to a type of steric Poisson-Nernst-Planck equations with Dirichlet boundary conditions, which are applicable to ion channels. With numerically found multiple steady-state solutions, we obtain S-shaped current-voltage and current-concentration curves, showing hysteretic response of ion conductance to voltages and boundary concentrations with memory effects. Boundary value problems are proposed to locate bifurcation points and predict the local bifurcation diagram near bifurcation points on the S-shaped curves. Numerical approaches for linear stability analysis are developed to understand the stability of the steady-state solutions that are only numerically available. Finite difference schemes are proposed to solve a derived eigenvalue problem involving differential operators. The linear stability analysis reveals that the S-shaped curves have two linearly stable branches of different conductance levels and one linearly unstable intermediate branch, exhibiting classical bistable hysteresis. As predicted in the linear stability analysis transition dynamics, from a steady-state solution on the unstable branch to one on the stable branches, are led by perturbations associated to the mode of the dominant eigenvalue. Further numerical tests demonstrate that the finite difference schemes proposed in the linear stability analysis are second-order accurate. Numerical approaches developed in this work can be applied to study linear stability of a class of time-dependent problems around their steady-state solutions that are computed numerically.

Stability analysis of multiple solutions in case of a stretched nanofluid flow obeying Corcione's correlation: An extended Darcy model

AbstractThe bi‐dimensional flow of a ‐water nanofluid perfusing a porous medium has been considered for investigation. The porous space is in contact with a constantly heated sheet stretching at a linear rate. To simulate the nanofluid flow through the pores, an extended Darcy model due to Brinkman and Forchheimer is utilized considering porosity and permeability effects in a convective environment. Corcione's model for effective dynamic viscosity of the nanoparticle mixture is exploited to deduce the effects of nanoparticle size on the flow. Multiple solutions to governing equations are obtained by availing the optimal homotopy asymptotic scheme and discussed for emerging parameters. A unique stable solution is determined availing a stability analysis approach. The heat movement rate is found to be increasing with the reduced nanoparticle size and the enhanced porosity of porous space.

A limit inferior ‐dependent average dwell time approach for stability analysis of switched systems

SummaryA novel concept of limit inferior‐dependent average dwell time (LDADT) is first proposed, which is a generalization of various existing concepts of dwell time. Based on the LDADT scheme and the multiple Lyapunov function approach, some new sufficient conditions for stability and stabilization of switched systems are established by introducing some inequalities. Those criteria acquired contain most of the established ones based on ADT, limiting ADT, mode‐dependent ADT,‐dependent ADT, etc. Specifically, the stability and stabilization criteria for switched linear systems are listed as linear matrix inequalities that can be examined and calculated easily by the LMI toolbox in Matlab. At last, three typical numerical examples are presented for illustrating the effectiveness and validity of the LDADT scheme presented in this paper.

An LMI based approach to stabilize a type of nonlinear uncertain neutral-type delay systems

This paper proposes a linear matrix inequality (LMI) based approach for stability analysis of a type of nonlinear uncertain neutral-type delay systems. The delays in states, state derivatives and inputs are known and constant. By constructing a Lyapunov–Krasovskii functional (LKF), a stability criterion in the form of LMI is derived. In this paper, we treat these nonlinear terms to be norm-bounded and construct a Lyapunov matrix inequality considering system states, delayed states, delayed state derivatives, and delayed inputs. The stability criterion of this nonlinear neutral-type delay system is then obtained. To this end, a numerical example is given to demonstrate the feasibility of the proposed approach. The developed method for stability analysis can potentially be applied to critical real-world applications such as the down-hole drilling system.