Nonfragile robust exponential stabilization of nonlinear uncertain switched systems with actuator saturation

Abstract

For nonlinear uncertain switched systems, the problem of how to overcome the controller vulnerability is studied when the actuator saturation is considered. The sufficient condition for guaranteeing nonfragile robust exponential stabilization of the system is derived by using the method of minimum dwell time. Then, a switching law and the nonfragile state feedback controllers are designed such that the closed‐loop system can be robustly exponentially stabilized at the origin. Next, when some scalar parameters of the closed‐loop system are given, the design issue of the nonfragile state feedback controllers, which aim at enlarging the estimation of domain of attraction for closed‐loop system, is transformed into a convex optimization issue with linear matrix inequalities (LMI) constraints. Finally, an example is given to verify the effectiveness of the proposed method.

Robust exponential stabilization and L2‐gain analysis for saturated switched nonlinear systems subject to actuator failure under asynchronous switching

“…There may be many ellipsoids that satisfy the invariant set condition in Theorem 1, we would like to choose the “largest” one from among them to maximize the estimation of domain of attraction. In the literature (e.g., see References 2,30,31), the largeness of a set is usually measured by its volume or shape. Here, we maximize the estimation of the domain of attraction for the closed‐loop system () by taking the shape of a set into consideration.…”

“…At the same time, the system has a class of logical rules to decide which subsystems to run, so that the whole switched system can operate properly. [1][2][3][4][5] On the other hand, stability is a fundamental property of switched systems, so there are research methods on stability that have received much attention in recent years. For instance, the common Lyapunov functions method to investigate the stabilization problem of systems was proposed in References 6 and 7.…”

“…Switched systems consists of a set of continuous or discrete‐time subsystems, which are mathematically described by a series of differential or difference equations, respectively. At the same time, the system has a class of logical rules to decide which subsystems to run, so that the whole switched system can operate properly 1‐5 . On the other hand, stability is a fundamental property of switched systems, so there are research methods on stability that have received much attention in recent years.…”

L2$$ {L}_2 $$‐gain analysis and fault‐tolerant control for nonlinear discrete‐time switched systems with time‐varying delay and actuator saturation

“…Hu et al 20 first proposed this method for estimating the domain of attraction of a discrete linear system under saturated linear feedback by deriving a simple condition to determine whether a given ellipsoid is contractively‐invariant. Wang and Zhang 21 used convex packet representation to deal with the actuator saturation problem and investigated the non‐fragile control problem for nonlinear switching systems by means of the Lyapunov function method and the minimum dwell time strategy. Another method is to design anti‐windup compensators to minimize the effects of saturation.…”

An anti‐windup and backlash compensation‐based finite‐time control method for performance enhancement of a class of nonlinear systems

“…For a nonlinear system with input saturation, a dynamical anti-windup compensator was employed to enlarge domain of attraction [23]. For some nonlinear uncertain switched systems with input saturation, switched non-fragile state feedback controllers were introduced to enlarge domain of attraction [24,25]. So, the given anti-windup approaches in the literature either improve the performance or enlarge the domain of attraction.…”