Robust stabilization of a class of switched linear systems

2003 ◽  
Author(s):  
Xiaoli Zhang ◽  
Jun Zhao
Keyword(s):  
Linear Systems ◽  
Robust Stabilization ◽  
Switched Linear Systems

Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach

2005 ◽  
Vol 128 (3) ◽  
pp. 696-700 ◽  
Author(s):  
Zhijian Ji ◽  
Xiaoxia Guo ◽  
Long Wang ◽  
Guangming Xie
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Robust Stabilization ◽  
Disturbance Attenuation ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Multiple Lyapunov Functions ◽  
Switched Linear Systems ◽  
Switched State Feedback

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.

scholarly journals Robust State Feedback Stabilization of Uncertain Discrete-Time Switched Linear Systems Subject to Actuator Saturation

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Xinquan Zhang ◽  
Guoliang Wang ◽  
Jun Zhao
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Robust Stabilization ◽  
Domain Of Attraction ◽  
Feedback Stabilization ◽  
Multiple Lyapunov Functions ◽  
Switched Linear Systems ◽  
Lyapunov Functions Method

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.

scholarly journals Robust Stabilization of Controlled Positive Switched Linear Systems by Output Feedback

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jinjin Liu ◽  
Ting Zhang
Keyword(s):  
Linear Systems ◽  
Output Feedback ◽  
Robust Stabilization ◽  
Average Dwell Time ◽  
Feedback Controllers ◽  
Switched Linear Systems ◽  
Closed Loop Systems ◽  
Polytopic Uncertainties ◽  
System States ◽  
Theoretical Results

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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