Robust stabilization of a class of switched linear systems

Author(s):  
Xiaoli Zhang ◽  
Jun Zhao
2005 ◽  
Vol 128 (3) ◽  
pp. 696-700 ◽  
Author(s):  
Zhijian Ji ◽  
Xiaoxia Guo ◽  
Long Wang ◽  
Guangming Xie

This paper addresses robust H∞ control and stabilization of switched linear systems with norm-bounded time-varying uncertainties. First, based on multiple Lyapunov functions methodology, a sufficient condition is derived for robust stabilization with a prescribed disturbance attenuation level γ only by employing state-dependent switching rules. Then the robust H∞ control synthesis via switched state feedback is studied. It is shown that a switched state-feedback controller can be designed to stabilize the switched systems with an H∞-norm bound if a matrix inequality based condition is feasible. This condition can be dealt with as linear matrix inequalities (LMIs) provided that the associated parameters are selected in advance. All the results presented can be regarded as an extension of some existing results for both switched and nonswitched systems.


2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Xinquan Zhang ◽  
Guoliang Wang ◽  
Jun Zhao

The robust stabilization problem is investigated for a class of discrete-time switched linear systems with time-varying norm-bounded uncertainties and saturating actuators by using the multiple Lyapunov functions method. A switching law and a state feedback law are designed to asymptotically stabilize the system with a large domain of attraction. Based on the multiple Lyapunov functions method, sufficient conditions are obtained for robust stabilization. Furthermore, when some parameters are given in advance, the state feedback controllers and the estimation of domain of attraction are presented by solving a convex optimization problem subject to a set of linear matrix inequalities (LMI) constraints. A numerical example is given to show the effectiveness of the proposed technique.


2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jinjin Liu ◽  
Ting Zhang

This study focuses on the controller synthesis issues for constrained switched linear systems with uncertainties under mode-dependent average dwell time (MDADT) switching strategy. First, output feedback controllers ensure that the closed-loop systems are positive and asymptotically stable. Second, the bounded controllers are acquired based on system states with interval and polytopic uncertainties. Also, the proposed approach can be applied to the systems with the constrained output. Then, the presented conditions can be formulated in terms of linear programming. Finally, illustrative example is provided to show the effectiveness of the theoretical results.


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