Universal construction of control Lyapunov functions for multi-input linear systems

2008 ◽  
Author(s):  
Cai Xiushan
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
Universal Construction

Minkowski and Lyapunov Functions in Contractive Sets Characterization for Discrete-Time Linear Systems

2021 ◽  
Author(s):  
Mihaela-Hanako Matcovschi ◽  
Marius Apetrii ◽  
Octavian Pastravanu ◽  
Mihail Voicu
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Time Linear

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.

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