On Stabilization of Linear Switched Singular Systems via P-D State Feedback

Abstract

Impulsive phenomenon and state jumps at switching instants are inevitable control difficulties in the study of stability for switched singular systems. Proportional-derivative (P-D) state feedback may be an effective way to eliminate impulsive behaviors and state jumps. In this work, the problem of stabilization is studied for switched singular systems in the continuous-time case and discrete-time case. A synchronous design method of P-D state feedback controllers is proposed by introducing some free-weighting matrices. Based on P-D state feedback, some sufficient conditions, which can guarantee that the closed-loop systems are normal and stable (NS), are obtained by using multiple Lyapunov functions. Compared with step-by-step design, synchronous design brings more freedom to the design of P-D state feedback controllers and can better improve the dynamic performance of the systems. Finally, simulation examples are given to demonstrate the effectiveness of the proposed methods.INDEX TERMS Switched singular systems, normal and stable, P-D state feedback, synchronous design.

Robust Output Strictly Passive H-Infinity Control of Uncertain Switched Singular Systems

“…Many real-world systems can be modelled as switched singular systems [3], such as switching power converters, networked control systems, traffic systems. In recent years, switched singular systems have attracted considerable attention of many scholars, and plenty of research results have been reported [1]- [6].…”

“…For any two singular subsystems, due to the existence of algebraic equations, the state variables at switching points may be not the consistent initial condition of the next activated subsystem, which will inevitably lead to state jump at the switching instant [9]. Simple state feedback or output feedback can hardly eliminate the impulsive behaviors and state jumps at switching instants [6]. Therefore, many research results on switched singular systems were obtained under assumptions that the states do not jump at switching instants [14], [20], [21] and all singular subsystems are impulse-free [22], [23].…”

“…The function of impulsive controllers is to reset the state variables at switching instants, so as to eliminate or reduce the state jumps and impulsive behaviors. Note that it is difficult to determine the switching instants in the complex situation [6]. Therefore, hybrid impulsive controllers can not solve the problems well in some cases.…”

“…Based on the above analysis, PD-SF control was applied to study switched singular systems for the first time in [26] and the idea of step-by-step design for controllers was proposed. Based on [26], a method of synchronous design of PD-SF controllers was proposed in [6] introducing some appropriate free-weighting matrices, and the stability problems of continuous-time and discretetime linear switched singular systems were studied. It should be pointed out that uncertainties were not considered in [6] and [26].…”

“…Based on [26], a method of synchronous design of PD-SF controllers was proposed in [6] introducing some appropriate free-weighting matrices, and the stability problems of continuous-time and discretetime linear switched singular systems were studied. It should be pointed out that uncertainties were not considered in [6] and [26]. Therefore, the designed controllers may fail if the system matrices have parameter perturbations.…”