Stability Criteria For Systems Research Articles

State observer‐based predictive proportional‐integral tracking control for fuzzy input time‐delay systems

SummaryThis study emphasis on the problem of state tracking and disturbance attenuation for Takagi‐Sugeno fuzzy based model with input time‐delay via improved extended state observer based predictive proportional‐integral tracking control. To be precise, a predictive proportional‐integral tracking controller is formulated by implementing the Smith‐Predictor strategy to restrain the influence of input time‐delay. Then, with the aid of improved extended state observer, the lumped disturbance is estimated and it is combined with the predictive proportional‐integral tracking control for disturbance attenuation. Further, closed‐loop control‐system is considered to ensure the satisfactory state tracking results for the considered system regardless of time‐delay in the control input and lumped disturbances. Meanwhile, based on the Lyapunov theory approach, the stability criteria for the proposed system are formulated in terms of linear matrix inequalities following which the gain matrices are derived. Finally, in order to evident the supremacy of the proffered control system, two numerical simulation results are provided.

A Novel Approach for Adaptive Partial Sliding Mode Controller Design and Tuning in Non-Minimum Phase Switch-Mode Power Supplies

In this article, a novel systematic approach is proposed for a partial sliding mode controller (SMC) design and tuning in non-minimum phase switch-mode power supplies (SMPS). To achieve a more simplified controller in comparison with the conventional SMCs, the partial SMC (PSMC) is introduced in this article, which just requires a part of the sliding surface for controller formulation. The accuracy of the developed PSMC is proved mathematically within the entire range of operation. Since the control parameters of the PSMC are not selected by trial and error, it can maintain the stability and robustness of the closed-loop system in a broad operational range. In this regard, and to develop a systematic approach for robust control of SMPS, a constant frequency equivalent SMC is designed using the converter nominal parameters. Then, the extracted controller is combined with an adaptive component to ensure asymptotical stability against load and line changes. Considering the Lyapunov stability criteria for nonlinear systems, it is proved that the presented SPMC can be used for output voltage regulation in both discontinuous and continuous operating modes with zero steady state error. To avoid the trial and error method during the controller tuning and parameters selection, the system characteristic equation is extracted using the Jacobian approach. Considering the roots of the characteristic equation and the stable range of the closed-loop system, the controller parameters are tuned. Furthermore, in addition to simulation, the developed approach is evaluated practically using the TMS3220F2810 digital signal processor. It is shown that the dynamic response of the proposed approach is faster than the standard double-loop SMC during load and line changes. Additionally, it is seen that the developed controller is robust against model changes in both continuous and discontinuous operations.

Input-to-State Stability for Time-Delay Systems With Large Delays

In this article, we consider the input-to-state stability (ISS) problem for a class of time-delay systems with intermittent large delays, which may cause the invalidation of traditional delay-dependent stability criteria. The topic of this article features that it proposes a novel kind of stability criterion for time-delay systems, which is delay dependent if the time delay is smaller than a prescribed allowable size. While if the time delay is larger than the allowable size, the ISS can be preserved as well provided that the large-delay periods satisfy the kind of duration condition. Different from existing results on similar topics, we present the main result based on a unified Lyapunov-Krasovskii function (LKF). In this way, the frequency restriction can be removed and the analysis complexity can be simplified. A numerical example is provided to verify the proposed results.

A general framework for robust stability analysis of neural networks with discrete time delays

Robust stability of different types of dynamical neural network models including time delay parameters have been extensively studied, and many different sets of sufficient conditions ensuring robust stability of these types of dynamical neural network models have been presented in past decades. In conducting stability analysis of dynamical neural systems, some basic properties of the employed activation functions and the forms of delay terms included in the mathematical representations of dynamical neural networks are of crucial importance in obtaining global stability criteria for dynamical neural systems. Therefore, this research article will examine a class of neural networks expressed by a mathematical model that involves the discrete time delay terms, the Lipschitz activation functions and possesses the intervalized parameter uncertainties. This paper will first present a new and alternative upper bound value of the second norm of the class of interval matrices, which will have an important impact on obtaining the desired results for establishing robust stability of these neural network models. Then, by exploiting wellknown Homeomorphism mapping theory and basic Lyapunov stability theory, we will state a new general framework for determining some novel robust stability conditions for dynamical neural networks possessing discrete time delay terms. This paper will also make a comprehensive review of some previously published robust stability results and show that the existing robust stability results can be easily derived from the results given in this paper.

Stability criteria for time-varying delay systems via an improved reciprocally convex inequality lemma

This paper investigates the stability analysis issue of time-varying delay systems via a novel reciprocally convex inequality lemma(RCIL). First, a novel reciprocally convex combination method is proposed by introducing a matrix-valued polynomial. Some previous methods are encompassed in the proposed method as special examples. Then, a newly asymmetric Lyapunov-Krasovskii(L-K) functional is presented via introducing some delay-product terms, which develop additional delay convexity information. Moreover, the proposed L-K functional and RCIL are amalgamated to develop new stability conditions. Finally, numerical examples and simulation experiments show the advancement of the proposed method.

A new design method to global asymptotic stabilization of strict-feedforward stochastic nonlinear time delay systems

The stabilization problems of stochastic nonlinear systems remain challenging because many new obstacles will be encountered and need to be cautiously handled. This paper discusses the global asymptotic stabilization problem of stochastic nonlinear systems which possess strict-feedforward structure and multiple time delays. In the first place, we are trying to transform the considered system into an equivalent one by constructing the novel parameter-dependent state feedback controller and the suitable coordinate transformation. And then, through using the stochastic time delay system stability criterion and introducing the proper Lyapunov–Krasovskii functional, the global asymptotic stability of stochastic closed-loop system is proved. Finally, simulation results show the effectiveness of the parameter-dependent state feedback controller.

Input-to-state practical stability criteria of non-autonomous infinite-dimensional systems

We develop tools for the investigation of input-to-state practical stability (ISpS) and integral input-to-state practical stability (iISpS) of non-autonomous infinite-dimensional systems in Banach spaces. Sufficient conditions of ISpS and iISpS are given based on indefinite Lyapunov functions. The practical stability analysis is accomplished with the help of scalar practical stable functions. Then, a construction of ISpS Lyapunov function for a class of non-autonomous evolutions equations is provided in Hilbert spaces. We propose the ISpS Lyapunov methodology to make it suitable for the analysis of ISpS w.r.t. inputs from -spaces. Furthermore, we illustrate the theory with an example of a semi-linear reaction-diffusion equation.

Almost sure stability criterion for continuous-time linear systems with uniformly distributed uncertainty

Assuming the uncertain parameter of a linear polytopic system to be uniformly distributed, we can prove that the system is almost sure exponentially stable if and only if its averaging system is stable. Computing the mathematical expectation of the state-transition matrix and characterizing the martingale structure embedded in its variance is the key for deriving this stability criterion.

New stability criteria for systems with an interval time-varying delay

<abstract><p>This paper studies the stability analysis of systems with an interval time-varying delay. First, some new integral inequalities are introduced. Second, based on these new integral inequalities, some less conservative stability criteria are introduced in terms of the linear matrix inequalities. Finally, the merits of the stability criteria are shown via two numerical examples.</p></abstract>

Weighted input-to-output practical stability of non-autonomous infinite-dimensional systems with disturbances

In this paper, we introduce a new concept of weighted input-to-output practical stability (WIOpS) and weighted integral-input-to-output practically stable (WiIOpS) for non-autonomous infinite-dimensional systems with disturbances. By using the notion of practical stable scalar functions, sufficient conditions for WIOpS and WiIOpS are derived. As a result, the robust global asymptotic output practical stability criteria of non-autonomous infinite-dimensional systems with zero input is also established via an indefinite Lyapunov function. Thus, we study the UWISpS of non-autonomous nonlinear evolution equations. Moreover, we discuss UWISS and UWiISS for linear non-autonomous infinite-dimensional control systems. A feedback law is provided for a class of semi-linear evolution equations by which the closed-loop system is uniform input-to-state practical stable (UISpS) with respect to disturbances acting in the input. Two examples are given throughout the paper to illustrate the theoretical results.

Tracking Control of Quadrotor with Intermittent Target Measurements: A Stochastic Switched Systems Approach

This paper is devoted to the investigation of target tracking control of quadrotor with intermittent measurements, i.e., the measurements of target position are not continuously available. A stochastic switched systems approach is utilized to formulate such a tracking process of quadrotor by splitting it into two modes according to whether the measurements are available. The mode switching of the underlying system is subject to a Markov process to account for the inherent non-memory randomness of the dwell time of each mode, in contrast with the existing studies that impractically require the duration of the measurements to be greater than a given constant. The stability criteria for the underlying system are derived, upon which a switched controller is designed for the quadrotor position control, rather than the determination of the bounds of the dwell time for given pre-designed controllers in each mode. Simulations are presented to demonstrate the effectiveness of the developed theoretical results and the superiority of the designed switched controller for tracking control of quadrotor with intermittent target measurements.

Delay-Dependent Stability Condition in Finite Frequency Domain: Input-Output Approach

Over finite frequency ranges, this study analyzes delay-dependent stability criteria for time-varying delay systems. To develop new delay-dependent stability conditions in finite frequency domains for the continuous time-varying delay systems, we construct an input-output technique for delay-dependent systems utilizing the two-term transformation model paired with Scaled-Small Gain (SSG) approach. Sufficient conditions are obtained and described in terms of linear matrix inequalities (LMIs) constraints based on a novel delay-dependent finite frequency inequality. As an illustration, a numerical example has been supplied to test the correctness of the current approach.

A Class of Inertial Measurement Units for Low-Noise Angular Velocity Estimation

An Inertial Measurement Unit (IMU) architecture estimating angular velocity is introduced. It expands the concept of multi-accelerometers gyroscope-free IMUs (GF-IMUs), taking advantage of their excellent noise performance and resolving their inability to compensate for accelerometers’ bias and their requirement for specific accelerometers placement, which makes GF-IMUs inappropriate for real world applications. It does so by embedding the accelerometers in a low-bandwidth closed-loop configuration with a three-axis gyroscope and by addressing the complete non-linear dynamics. Extensive theoretical analysis provides a complete framework for designing low-noise IMUs including sufficient stability criteria for the non-linear system’s dynamics. Simulation and experimental results support the theoretical analysis and indicate that even a minimal system using the proposed architecture can outperform the gyroscope in noise performance by at most 15dB in some frequency range.

State Estimation for a Class of Discrete-Time BAM Neural Networks With Multiple Time-Varying Delays

For a class of discrete-time bidirectional associative memory neural networks (DTBAMNNs) with multiple time-varying delays, the issue of state estimation is studied. By propose a mathematical induction method, we first investigate novel delay-dependent and -independent global exponential stability (GES) criteria of the error system. The obtained GES criteria are described by linear scalar inequalities. Then, a state observer is derived via the theory of generalized matrix inverses. These exponential stability conditions are very simple, which is convenient to verify based on the standard software tools (for example, YALMIP). Finally, we present two illustrative examples to present the effectiveness of the theoretical results.

Underconstrained Cable-Driven Parallel Suspension System of Virtual Flight Test Model in Wind Tunnel

An underconstrained cable-driven parallel robot (CDPR) suspension system was designed for a virtual flight testing (VFT) model. This mechanism includes two identical upper and lower kinematic chains, each of which comprises a cylindrical pair, rotating pair, and cable parallelogram. The model is pulled via two cables at the top and bottom and fixed by a yaw turntable, which can realize free coupling and decoupling with three rotational degrees of freedom of the model. First, the underconstrained CDPR suspension system of the VFT model was designed according to the mechanics theory, the degrees of freedom were verified, and the support platform was optimized to realize the coincidence between the model’s center of mass and the rotation center of the mechanism during the motion to ensure the stability of the support system. Finally, kinematic and dynamical modeling of the underconstrained CDPR suspension system was conducted; the system stiffness and stability criteria were deduced. Thus, the modeling of an underconstrained, reconfigurable, passively driven CDPR was understood comprehensively. Furthermore, dynamic simulations and experiments were used to verify that the proposed system meets the support requirements of the wind tunnel-based VFT model. This study serves as the foundation for subsequent wind tunnel test research on identifying the aerodynamic parameters of aircraft models, and also provides new avenues for the development of novel support methods for the wind tunnel test model.

Finite-time control for discrete-time nonlinear Markov switching LPV systems with DoS attacks

This work studies the finite-time control problem for discrete-time nonlinear Markov switching linear parameter varying (LPV) systems with denial-of-service (DoS) attacks. The aperiodic DoS attacks are introduced into the systems with partially unknown transition probabilities. First, considering the characteristics of aperiodic DoS attacks, an appropriate feedback controller is designed according to that whether it is attacked or not. Furthermore, the finite-time stability criteria of closed-loop system are derived by means of iterative technique and multiple Lyapunov functions. Finally, a turbofan engine model is taken as an example to verify the effectiveness and feasibility of the proposed finite-time control method.

Practical stability of continuous-time stochastic nonlinear system via event-triggered feedback control

This paper develops new practical stability criteria for continuous-time stochastic nonlinear system with uncertainties and external disturbances. Two cases of the system are considered: the system with state-dependent disturbance and the system with state-independent disturbance. Based on the event-triggered mechanism and Lyapunov function, we establish the input-to-state practical exponential stability in mean square for each case of the system. The obtained results improve some previous works in the literature. Finally, several examples are given to show the effectiveness and practicability of the main results.

Contraction criteria for incremental stability of differential systems with discontinuous right-hand sides

Incremental stability analysis, which plays a crucial role in dynamical systems, especially nonlinear systems, has attracted more and more concern for its applications in real world control systems nowadays. This paper presents a constructive approach to derive sufficient conditions for incremental exponential stability of the Filippov solutions of a class of differential systems with discontinuous right-hand sides, by introducing a sequence of continuous dynamical systems which is uniformly contracting and approximating the Filippov systems in terms of the evolution map graphs. Afterwards, several applications of the derived theoretical results are explored. Some specific classes of control dynamical systems with discontinuous right-hand sides are studied and relative detailed conditions are presented to show the power of the present approach to investigate the stability of switched dynamical systems, Hopfield neural network with discontinuous activations and sliding mode control.

A New Asymptotic Stability Criterion for Linear Discrete-Time Systems

In this brief, a new criterion to determine whether the roots of a polynomial <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p(z^{-1})$ </tex-math></inline-formula> with real coefficients are strictly inside the unit circle is presented. It is based on representing the polynomial in a form corresponding to the characteristic polynomial of a closed-loop systems in which all-pass transfer functions are included in both direct chain and feedback loop. The novel and simple criterion for assessing the asymptotic stability of linear discrete-time systems is proved applying the small-gain theorem in the discrete-time domain.

A PSO-Based Approach for Optimal Allocation and Sizing of Resistive-Type SFCLs to Enhance the Transient Stability of Power Systems

Transient stability improvement of power systems in the event of short-circuit faults has always been an important issue in power systems analysis and studies. Resistive-type superconducting fault current limiters (RSFCL), owing to their capability in restricting fault currents, have been often taken into account as an efficient method to improve the transient stability of a power system. Regarding technical constraints as well as economic concerns, optimal allocation and sizing of RSFCLs in a power system play a crucial role in their efficient utilization. This paper aims to continue the authors’ previous work and enhance the transient stability of power systems by proposing an optimization approach for optimal sizing and the allocation of various candidate numbers of RSFCLs, as the most employed type of SFCL and the most efficient one in transient stability improvement. To solve the optimization problem, a PSO-based algorithm is solved in MATLAB through an objective function and related constraints. The efficacy of the proposed algorithm is evaluated by numerical studies on the IEEE 39-Bus New England system in various scenarios through the assessment of critical fault clearing time (CCT) as well as the generators rotor angle deviations as two crucial criteria for the transient stability of power systems. Simulating the optimization results in DIgSILENT Power Factory indicates an evident enhancement of the power system transient stability via employing optimized RSFCLs resulted from the proposed optimization algorithm. Moreover, the level of transient stability enhancement highly depends on the number of optimized RSFCLs employed in the power system. The results of this paper present a helpful guideline for power system planners to select an appropriate stability scheme based on RSFCLs besides other related technical and economic issues.