Stability Of Switched Systems Research Articles

On Stability and State-Norm Estimation of Switched Systems Under Restricted Switching

On Stability and State-Norm Estimation of Switched Systems Under Restricted Switching

Almost Sure Stability and Stabilization of Composite Switched Systems With Persistent Dwell Time Constraint.

This article is devoted to the exponential almost sure (EAS) stability and stabilization of continuous-time composite switched systems (CSSs) by employing a novel dual-switching mechanism, which incorporates both persistent dwell time (PDT) switching and a set of Markov processes. The interrelation between the parameters under the PDT constraint is established by ensuring that switching frequency remains within the maximum permissible range, which serves as a pivotal consideration in the stability analysis of CSSs subject to above-mentioned dual-switching mechanism. Furthermore, the sufficient conditions for achieving EAS-stability and stabilization of CSSs are established with the designed switching strategy. Our results, in contrast to previous works that are special cases of our study, are more general and less conservative. Three examples are presented to validate the developed theoretical results.

Finite-time Stabilization of Fractional-order Impulsive Switched Systems With Saturated Control Input

Finite-time Stabilization of Fractional-order Impulsive Switched Systems With Saturated Control Input

Simultaneous Stabilization of Second Order Linear Switched Systems Based on Superstability and D-Decomposition Technique

Simultaneous Stabilization of Second Order Linear Switched Systems Based on Superstability and D-Decomposition Technique

Simultaneous Stabilization of Second Order Linear Switched Systems Based on Superstability and D-Decomposition Technique

Simultaneous Stabilization of Second Order Linear Switched Systems Based on Superstability and D-Decomposition Technique

Kalman Filter of Switching System Under Hybrid Cyber Attack

Potential malicious attacks have been a significant security concern for network system applications. However, there are few studies on filtering for hybrid network attacks in switching systems. This paper considers a Kalman filtering problem for the switched systems that suffer from deception attacks and denial-of-service attacks. A new network transmission model for switching systems is established. Then, based on the minimum mean square error criterion, a Kalman filter with low conservatism is designed for the discrete-time switched system. The newly switched Kalman gain matrix is deduced including the random variation of the switching signal after being attacked by the network. Finally, the effectiveness of the proposed filter is verified by the numerical simulation. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —A switching system is considered to be a typical hybrid system. As it often works in a network environment, the switching signal is vulnerable to the network and thus to various cyber-attacks (e.g. spoofing attacks and denial-of-service attacks). Few studies have been conducted on the impact of switching signals in network transmission. To address this problem, this paper proposes a Kalman filter design method with low conservativeness, which describes network attacks and data loss by building a Kalman filter model associated with the switching signal in terms of satisfying Bernoulli random variables. For practitioners, the ability to recover data to a certain extent when the data transmission is affected by different network attacks will save a lot of costs and is important for improving the stability and performance of switching systems. Our future work will aim to improve the performance of different filtering algorithms under different cyber-attacks.

Exponential Stabilization of Polynomial Fuzzy Positive Switched Systems With Time Delay Considering MDADT Switching Signal

Exponential Stabilization of Polynomial Fuzzy Positive Switched Systems With Time Delay Considering MDADT Switching Signal

Global Stability of a Second-Order Affine Switching System

Global Stability of a Second-Order Affine Switching System

Construction of invariant Lyapunov norms for planar switching systems

We consider the problem of the stability of linear dynamical switching systems. It is known that an irreducible $d$-dimensional system always has an invariant Lyapunov norm (a Barabanov norm), which determines the stability of the system and the rate of growth of its trajectories. We prove that in the case of $d=2$ the invariant norm is a piecewise analytic function and can be constructed explicitly for every finite system of matrices. The method of construction, an algorithm for computing the Lyapunov exponent and a way for deciding the stability of the system are presented. A complete classification of invariant norms for planar systems is derived. A criterion of the uniqueness of an invariant norm of a given system is proved, and some special norms (norms generated by polygons and so on) are investigated. Bibliography: 30 titles.

Non-fragile Robust Stabilization of Nonlinear Uncertain Switched Systems with Actuator Saturation

Non-fragile Robust Stabilization of Nonlinear Uncertain Switched Systems with Actuator Saturation

Finite-Time Stabilization of Switched Systems Under Mode-Dependent Event-Triggered Impulsive Control

This article studies the event-triggered finite-time stabilization problem of nonlinear switched systems in which the time derivatives of Lyapunov functions of modes are indefinite. Based on a mode-dependent average dwell time constraint and event-triggered impulsive control (ETIC) strategy, a new type of the mode-dependent event-triggered mechanism (MDETM) which can efficiently avoid Zeno behavior for switched systems is presented. Some Lyapunov-based criteria for finite-time stability (FTS) and finite-time contractive stability (FTCS) are obtained, respectively, where a relationship between the prescribed bound and event-triggered mechanism is established. Then, we apply these proposed ETIC strategies to impulsive switched systems and design a class of LMI-based MDETMs to guarantee the FTS/FTCS property. Finally, the effectiveness of presented ETIC strategies is illustrated by two examples.

Stability of Switched Systems with Time-Varying Delays under State-Dependent Switching

This paper studies the stability of linear switched systems with time-varying delays and all unstable subsystems. According to the largest region function strategy, the state-dependent switching rule is designed. By bringing in integral inequality and multiple Lyapunov-Krasovskii functionals, the stability results of delayed switched systems with or without sliding motions under the designed state-dependent switching rule are derived for different assumptions on time delay. Several numerical examples are employed to show the effectiveness and superiority of the proposed results.

Input–Output Finite-Time Asynchronous SMC for Nonlinear Semi-Markov Switching Systems With Application

This article investigates the input–output finite-time stability (IO-FTS) for nonlinear hidden semi-Markov switching systems (S-MSSs) via the asynchronous sliding mode control (SMC) approach. Under the assumption that a detector is set up to estimate the mode value, the mode of the original system is not directly accessible. The asynchrony between the system and controller is described as a hidden semi-Markov model (HSMM). Many practical factors, such as semi-Markov switching parameters, finite-time interval, asynchronous phenomenon, uncertain parameters, and nonlinearity, are taking into account during the SMC design process. We aim to design an efficient finite-time asynchronous SMC scheme under a hidden semi-Markov switching effect. A novel sliding switching surface (SSS) is constructed, in which the SMC law rises asynchronously with original S-MSSs. Then, by means of finite-time stability, an asynchronous SMC law is synthesized to guarantee that the associated hidden S-MSSs fulfill the reaching condition within a finite time. Furthermore, sufficient conditions are derived in view of the IO-FTS of sliding mode dynamics under the framework of a novel inequality lemma. Results are given for the application of this control design method to a single-link robot arm model (SLRAM).

Adaptive compensation of uncertain Euler–Lagrange systems with multiple time-varying actuator faults

This work proposes the command tracking problem for uncertain Euler–Lagrange (EL) systems with multiple partial loss of effectiveness (PLOE) actuator faults. Compared to existing fault-tolerant controllers for EL systems, the proposed adaptive controller accounts for parametric uncertainties in the system and multiple time-varying actuator fault parameters. The proposed method can also handle an infinite number of fault cases. The closed-loop fault-tolerant system is treated as a switched dynamical system, and a switched system stability is established using multiple Lyapunov functions. It is shown that all signals are bounded in each sub-interval and at the switching instances, and asymptotic tracking can be obtained only for a finite number of fault occurrences, whereas tracking error is bounded for the infinite case. Finally, a simulation example on a robotic manipulator is presented to show the effectiveness of the proposed method.

Sliding Mode Observer-Based Fault Detection in Continuous Time Linear Switched Systems

This paper studies the problem of fault detection for continuous time linear switched systems in the presence of disturbance. For this purpose, a fault detection sliding mode observer approach is designed to generate the residual signal. To minimize the effect of disturbance from the residual, the problem is formulated into H∞ filtering technique to increase more robustness. To deal with the issue of the switched systems stability, the Lyapunov-Krasovskii functional method is utilized along with average dwell time, and linear matrix inequalities are formulated to derive the sufficient conditions. The residual signal is evaluated, and an adaptive threshold is computed for both modes of the switched system. Finally, a simulation example for a case study of boost converter and a numerical example with both abrupt and incipient faults are illustrated to prove the efficacy of the proposed method.

Stability of Switched Systems with Multiple Equilibria: A Mixed Stable-Unstable Subsystem Case

Stability of Switched Systems with Multiple Equilibria: A Mixed Stable-Unstable Subsystem Case

Stabilization of Uncertain Switched Systems with Frequent Asynchronism via Event‐Triggered Dynamic Output‐Feedback Control

This article investigates stabilization for a group of uncertain switched systems with frequent asynchronism. Without the limitation of minimum residence time, the average dwell‐time strategy makes it possible for switched systems with uncertain parameters to switch frequently over successive event intervals. Since it is highbrow and expensive to obtain the whole state information in practice, the dynamic output‐feedback controller is applied. With the aid of a controller‐pattern‐related Lyapunov functional and an event‐triggered dynamic output‐feedback controller, sufficient conditions are established to ensure the stability of the resulting uncertain closed‐loop system. To appropriately deal with the uncertain parameters, some inequalities of the linear matrix are tactfully utilized together with the Lyapunov functional and controller gains are constructed by the strategy of the block matrix. Furthermore, the presence of the lower boundary on adjacent event intervals is earnestly discussed to eliminate the Zeno behavior. Eventually, the feasibility and availability of the theoretical results are illuminated by a numerical simulation.

Smoothly Switched Adaptive Torque Tracking for Functional Electrical Stimulation Cycling

Motorized functional electrical stimulation (FES) cycling can serve as a rehabilitation strategy for individuals affected by neurological injuries. It is unique among human-robot interaction tasks because the cycle's motor must be simultaneously controlled alongside the rider's leg muscles (using neuromuscular electrical stimulation). In this letter, two tracking objectives are proposed for the FES cycle: 1) stimulate the rider's leg muscles to track a desired cadence, and 2) use the cycle's motor to indirectly track a desired torque with an adaptive admittance controller. A combined Lyapunov and passivity based switched systems stability analysis is conducted to prove the cycle's motor is able to globally exponentially track the admittance trajectory and stabilize the overall system. Additionally, this letter showcases a method for the rider to smoothly enable and disable torque tracking. Experiments are presented on four participants to show the efficacy of the controllers.

Updating [formula omitted] is significant to Caputo fractional order switching systems: A reply to Hu’s comments

This is to reply the concerns about our NAHS paper “Lyapunov and external stability of Caputo fractional order switching systems” pointed out by Hu in “Comments on ‘Lyapunov and external stability of Caputo fractional order switching systems”’ recently.

Stabilization of Nonlinear Switched Systems with Distributed Time-delay: The Discrete-time Case

Stabilization of Nonlinear Switched Systems with Distributed Time-delay: The Discrete-time Case