Problem Of Stability Analysis Research Articles

A POD Reduced Order Method Applied to an Instability Problem of Rayleigh–Bénard Convection

The application of a proper orthogonal decomposition (POD) reduced order method to a two-dimensional instability problem of Rayleigh–Bénard convection is described in this work. The partial differential equations that model the problem along with the corresponding eigenvalue problems of the linear stability analysis of stationary solutions are numerically solved for different values of the bifurcation parameter, i.e. the Rayleigh number [Formula: see text]. The POD reduced order method considers spaces derived from different stationary solutions depending on [Formula: see text] as snapshots. The eigenvalue with the largest real part and its corresponding eigenfunction are calculated for the POD solutions. The resulting matrices of the eigenvalue problems are low-dimensional. There is a drastic reduction in the computational cost.

Stability and Control of Fuzzy Semi-Markov Jump Systems Under Unknown Semi-Markov Kernel

This article investigates the stochastic stability analysis and stabilization problems for discrete-time Takagi–Sugeno fuzzy semi-Markov jump systems with upper-bounded sojourn time. The fuzzy rules can be different for different system modes. Consequently, the membership functions for fuzzy rules are dependent on the system modes. Allowing for the fact that semi-Markov kernel (SMK) are difficult to fully obtain in practice, the elements in the SMK of the underlying systems are deemed to be partly known, which is more general than both semi-Markov jump systems with completely available SMK and Markov jump systems with unknown transition probabilities. Afterward, the stability and stabilization conditions are established by part of the known SMK information and then by all the known SMK information. In the end, the validity and the superiority of our proposed theoretical results are exemplified via a single-link robot arm and a truck-trailer model.

Single-Input Single-Output System with Multiple Time Delay PID Control Methods for UAV Cluster Multiagent Systems

Multiagent has become a multidomain intersecting hot issue as artificial intelligence technology has advanced in the industrial sector. Multiagent system creation control has lately undergone a lot of academic research, and it has got applications in a wide range of fields, including drag reduction, monitoring, telecommunications relay, and searching. A matrix theory using algebraic graph theory for automatic control principle learning is proposed based on multiagent system collaborative control strategy method to study the application of PID control method in human-machine cluster multi-intelligence system. The method first presents the determination of the stability set of the low-order controller parameters for the multidelay single-input single-output system with complex coefficients; through matrix theory, the multi-intelligence system is decomposed into multiple subsystems and the problem is transformed into subsystem stability analysis problem; thus, the complexity of the system is reduced. It has been proved that the power system device adopted by the UAV hardware platform can make the UAV flight time up to 24.7 min and additional load up to 1.5 kg. Based on the simulation analysis of PID control algorithm, the PID parameters of UAV are adjusted, which improves the parameter tuning efficiency and enhances the response speed of UAV to error and the stability of motion. The experimental findings suggest that the UAV hardware platform in the UAV control system has high dynamic performance. Good PID settings allow the UAV to respond to control orders quickly and correctly; also, the data received by the sensor decrease the complexity of operating several UAVs at the same time and minimize the operators’ burden.

Relaxed stability analysis and sampled-data controller design for networked control systems with network-induced delays

This paper is devoted to the stability analysis and sampled-data controller design problem for networked control systems subject to network-induced delays. The objective is to provide relaxed conditions in terms of linear matrix inequalities. Indeed, reducing the conservatism of such conditions allows to maximize the admissible range of the network-induced delays. To do so, an augmented Lyapunov–Krasovskii functional is proposed, which involves a novel augmented state vector to include as much as possible the information from the time-varying network-induced delay into the stability conditions, together with the use of extended Wirtinger-based inequalities, an extended reciprocal convexity approach and the Finsler’s lemma. Then, declined from the proposed stability conditions, new relaxed delay-dependent conditions for the design of networked sampled-data controllers are proposed. These allow to obtain simultaneously the controller gains and the maximal allowable bound of the network-induced delays with regards to its lower bound. Three illustrative examples are provided to show the effectiveness of the proposed networked control systems stability and controller design conditions, as well as to highlight the so raised conservatism improvements regarding the previous relevant results from the literature.

Anti-inertial loading platform: New method of resisting inertia in transport

To mitigate the disadvantages of cargo protection in the transportation industry, a vehicle-mounted loading platform that can offset the inertial force is proposed herein, and its prototype is built. This device solves the problem of inertia in cargo transportation using a novel concept. The device uses an accelerometer for signal acquisition and a brushless gear motor as the driving force. Based on the current acceleration value of the vehicle, the tilting angle of the loading platform is changed such that the resultant force of the loaded object is perpendicular to the loading platform. Prior to building the real prototype, a root locus analysis of the entire model is performed using the Simulink/Analysis tool. Subsequently, the method is optimized to solve problems in stability analysis. Finally, the prototype is evaluated in a pickup truck, and both the measured acceleration-angle curve and the actual performance of the prototype in the truck confirm excellent application value of the vehicle-mounted anti-inertial loading platform.

Lyapunov stability criteria in terms of class [formula omitted] functions for Riemann–Liouville nabla fractional order systems

This paper focuses on the problem of stability analysis for Riemann–Liouville nabla fractional order systems. On one hand, a useful comparison principle is built and then a rigorous proof is constructed for the well-known Lyapunov stability criterion in terms of class K functions. On the other hand, the constraint of the Lyapunov function is refined using a positive constant γ4 or a sequence h(k), resulting two practical theorems. Finally, three illustrative examples are given to show the applicability of the proposed method.

Searching Method of Critical Slip Surface of Slope Based on Improved Wolf Swarm Algorithm

Determining the critical sliding surface and calculating the safety factor of slope stability are the key problems of slope stability analysis. Firstly, according to the characteristics of the existing wolf swarm algorithm, an improved wolf swarm algorithm is proposed, which abandons the assumption of a circular sliding surface. Then, a multipoint spline curve is introduced to describe the shape of a slope sliding surface. The optimization of the curve can determine the critical slip surface of slope and avoid falling into the local optimum. This method is programmed and implemented in Python, and then, accuracy and reliability are verified through typical slope cases and engineering examples, and the sensitivity analysis of factors that have great influence is carried out. The research results show that the slope sliding surface search method based on the improved wolf swarm algorithm can effectively and quickly determine the critical sliding surface of the slope. Compared with traditional methods, it has higher convergence accuracy and reliability. It provides an effective method for slope stability analysis.

Bessel-type inequality in semi-inner-product spaces and its application to stability analysis of discrete-time systems with distributed delays

In this paper, a Bessel-type inequality in semi-inner produce (s.i.p.) spaces is presented to deal with the problem of stability analysis for a class of discrete-time systems with distributed delays. The main purpose of this paper is to obtain less conservative stability conditions for the investigated systems. For this purpose, a novel inequality (which is referred to as Bessel-type inequality in s.i.p. spaces) is constructed by combining the Bessel inequality and a set of polynomials which is pairwise orthogonal in a s.i.p. space. The proposed inequality is more general than the conventional Jensen-type inequality, which is, to the best of our knowledge, the only inequality to deal with the problem of stability analysis for discrete-time systems with distributed delays up to now. Based on the proposed inequality and the Lyapunov-Krasovskii stability theory, a stability condition is presented. Finally, a numerical example is given to indicate that the proposed method is able to effectively reduce the conservatism.

A unified framework of convex stability conditions for 2-D switched systems with stable or unstable modes

The discrete-time two-dimensional (2-D) switched system is a powerful tool to model many practical physical processes with abrupt changes. However, the stability analysis problem for 2-D switched systems struggles to provide a unified framework for stable or unstable modes. Users have to delicately tune lots of parameters to shape the Lyapunov function for each mode. Besides, the resulting stability conditions are non-convex and thus the feasibility highly depends on the tuning parameters. In this paper, we propose a unified stability framework for 2-D switched systems, formulated by the well-known Fornasini–Marchesini local state-space model and the Roesser model. The concepts called unit switching sequence (USS) and sequence generator are presented. A novel Lyapunov function is also accordingly established which views the switching sequence as a concatenation of USSs, different from the perspective that regards the switching sequence as a combination of subsystems in previous literatures. Upon this framework, a convex stability criterion is developed, and the conservativeness can be lowered by a lifting technique at the expense of a higher off-line computational complexity. The derived theories are further extended for a standard l2-gain which is achieved under restricted switching signals for the first time. Numerical examples are provided for validity verification, conservativeness comparison, and l2-gain computation.

Stability analysis of delayed neural networks: An auxiliary matrix-based technique

This paper revisits the problem of stability analysis for delayed neural networks (DNNs). By introducing a set of auxiliary vectors and slack matrices, an auxiliary matrix-based integral inequality (AMBII) is presented. The auxiliary matrix is composed of auxiliary vectors, slack matrix and time-varying delay. It can make a trade off between conservatism and complexity. By using AMBII, a less conservative stability criterion is obtained for DNNs in terms of linear matrix inequalities (LMIs). The effectiveness of the stability condition can be demonstrated by illustrating a numerical example.

Shear creep mechanical properties and damage model of mudstone in open-pit coal mine

Clarifying the shear creep characteristics of rock and scientifically analyzing its creep deformation law is the key to solving the problem of safe construction and long-term stability analysis of the open-pit coal slope rock mass. Shear creep tests were carried out on mudstone from an open-pit coal mine in Eastern Mongolia to reveal the creep characteristics of mudstone under different normal and shear stresses. Based on the classical Nishihara model, a new composite six-element nonlinear shear creep damage model is established by introducing nonlinear elastomers. Using the least square method, model verification and parameter identification are carried out on the variable test data. At the same time, the influence law of the model parameters on the rock creep deformation is analyzed according to the theoretical curve. The study results showed that the nonlinear shear creeps damage model could better describe the creep characteristics of rock different normal stress and shear stress levels, significantly the non-linear both the strain and time of attenuation creep and accelerated creep. The creep characteristics of the accelerated creep stage described by this model are better than those described by the classical Nishihara model. The model curve is consistent with the changing trend of the experimental data, and the degree of agreement is very high. The correlation coefficients are all above 0.98, which verifies the accuracy and rationality of the model. The influence law of creep parameters is analyzed. The parameters b and c increase nonlinearly with creep. The increase of λ accelerates the process of rock attenuation creep stage; the increase of η10 slows down the progress of rock decay creep stage; with the increase of α, the deformation and creep rate of rock in accelerated creep stage gradually increase. When η2 increases, the deformation in the acceleration stage decreases gradually. The research results can provide important theoretical support for the safe construction and long-term stability analysis of open-pit coal slope rock masses.

Novel Results for Markov Jump 2D Interfered Digital Filters with State-Delay and Saturation Nonlinearities

Existing results on [Formula: see text] stability analysis problems for 2D digital filters are limited to external interference and saturation arithmetic. Unfortunately, developed results so far are not sufficient to tackle Markovian jumping parameters (MJPs) and state-delay. Such stability problem for 2D digital filters under MJPs, saturation arithmetic, state-delay and external interference has not been considered in the existing literature. In this paper, novel [Formula: see text] performance analysis criterion is first proposed for 2D interfered digital filters in which state-delay, saturation nonlinearities and MJPs are considered. The mathematical model of the underlying 2D system is described by the Roesser model. Furthermore, improved [Formula: see text] performance analysis criterion over the existing result is also obtained for 2D interfered digital filters with saturation nonlinearities only. At the end, two examples are employed to illustrate the effectiveness of the devised stability results.

Sampled-data distributed control for homo-directional linear hyperbolic system with spatially sampled state measurements

This paper addresses the stability analysis problem for a class of linear hyperbolic systems with distributed controllers sampled in space and time. First, the considered system is recast in an equivalent form with a continuous time control loop and operators representing the discretization errors (spatio-temporal sampling errors). Then with the help of the Lyapunov–Razumikhin approach, the Rɛ-stability of the proposed linear hyperbolic systems of balance laws is verified via sufficient conditions. At last, the proposed method is illustrated numerically.

LMIs-based stability analysis and fuzzy-logic controller design for networked systems with sector nonlinearities: Application in tunnel diode circuit

In this article, the problem of exponential mean-square stability analysis is discussed for uncertain networked control systems expressed by a stochastic T-S fuzzy model. In general, the characteristics of random occurrence for multipath packet dropouts often exist in the signal transmission network. For dealing with this difficult point, a dynamic output feedback strategy combining stochastic Bernoulli theory is employed. Then, delay-dependent stability conditions are derived and closed-loop system is exponentially mean-square stable by designing fuzzy-basis-dependent Lyapunov functional. Furthermore, in terms of linear matrix inequalities (LMIs) technology, sufficient conditions are gained to guarantee the prescribed H-infinity performance. Different from previous literatures, the congruence transformation method is employed to determine controller gain matrices for reducing the computation complexity of solving LMIs. Finally, the proposed method is applied in tunnel diode circuit model to verify the applicability.

A traverse algorithm approach to stochastic stability analysis of Markovian jump systems with unknown and uncertain transition rates

This paper intents to investigate the problem of mean-square stability analysis of Markovian jump systems with generally unknown and uncertain transition rates. Different from pervious works that the transition rates from one mode to others may be partially unknown or uncertain, in this note, the case that the transition rates from one mode to others are totally unknown will be investigated. By means of transition rate estimation, two ways are provided to tackle with the totally unknown case. In general, five cases in the transition rates matrix are studied for the mean-square stability analysis, which almost have covered all types of generally unknown and uncertain transition rates. Simultaneously, corresponding conditions for checking the mean-square stability of the considered Markovian jump systems are developed for the five studied cases. Finally, numerical examples are provided to verify the effectiveness of the proposed results.

Learning‐based robust control methodologies under information constraints

Learning‐based robust control methodologies under information constraints

Stability analysis of positive systems with delayed impulses

This paper investigates the problem of the stability analysis for positive systems with stabilizing delayed impulses. First, the stability analysis problem is considered for positive systems, where impulse delay is assumed to be deterministic and the method of average impulsive delay (AID) is used to handle the time-delay term in impulses. Then, the stability analysis problem is studied for positive systems with stochastic impulsive delay, and the case is considered where the impulse delay is satisfied by Markov chain. Further, the criteria ensuring the globally exponential stability and the stochastically exponential stability are derived. Finally, two illustrative examples are presented to show the validity of the obtained results.

Improved stability criterion for distributed time-delay systems via a generalized delay partitioning approach

<abstract><p>This paper researches the problem of stability analysis for distributed time-delay systems. A newly augmented Lyapunov-Krasovskii functional (LKF) is first introduced via a generalized delay partitioning approach. Then, a less conservative stability criterion is derived by introducing a novel Jensen inequality to estimate the integral terms in the derivative of LKF. The stability condition is given in terms of linear matrix inequality. Finally, the merits of the obtained stability criterion is shown by a well-known example.</p></abstract>

Dynamic output-feedback control of continuous-time Lur'e systems using Zames-Falb multipliers by means of an LMI-based algorithm

This paper investigates the problems of stability analysis and control design for continuous-time Lur'e systems with slope bounded nonlinearities. Starting from a stability analysis condition from the literature, based on the real positivity and a bound to the L1 norm of a certain transfer function, new sufficient conditions are proposed in an augmented parameter space for the simultaneous existence of a stabilizing dynamic output-feedback controller and a Zames-Falb multiplier certifying the closed-loop stability. The matrices of the controller realization as well as of the Zames-Falb multiplier appear affinely in the conditions, being dealt with as optimization variables. Furthermore, no line search is required to enforce the L1 norm constraint. An iterative algorithm is constructed to solve the problem through semidefinite programming, providing dynamic controllers of any given order. The controller can take into account both the output of the linear part of the system and of the nonlinearity. Numerical examples illustrate the results.

An LMI Approach for Stability Analysis and Output-Feedback Stabilization of Discrete-Time Lur’e Systems Using Zames-Falb Multipliers

This letter investigates the problem of stability analysis and output-feedback stabilization of discrete-time Lur'e systems where the nonlinearity is odd and slope bounded. Using the linear matrix inequality (LMI) conditions from the literature to handle the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm and positive realness constraints, an iterative algorithm based on LMIs is constructed to assess stability through the existence of a Zames-Falb multiplier of any given order based on independent positive definite matrices for the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm and positive realness. More important, the method can also deal with output-feedback stabilization. Numerical examples illustrate the performance of the proposed approach when compared with other methods.