scholarly journals Stabilization and control Lyapunov functions for language constrained discrete-time switched linear systems

Automatica ◽  
2018 ◽  
Vol 93 ◽  
pp. 64-74 ◽  
Author(s):  
Mirko Fiacchini ◽  
Marc Jungers ◽  
Antoine Girard
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Switched Linear Systems ◽  
And Control

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.

Asynchronous H∞ filtering fault detection for discrete-time switched linear systems

2021 ◽  
pp. 014233122110320
Author(s):  
Jinjie Huang ◽  
Xianzhi Hao ◽  
Xiaozhen Pan
Keyword(s):  
Fault Detection ◽  
Linear Systems ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Evaluation System ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Switched Linear Systems

This article studies the asynchronous H∞ filtering fault detection for discrete-time switched linear systems with mode-dependent average dwell time (MDADT). Firstly, a series of mode-dependent fault detection filters are designed, and augmented with original switched systems to construct a residual evaluation system. However, in practice, the switching of the filter often lags behind the corresponding subsystem. To deal with this, the running time of the subsystem is divided into two parts: the matched and the mismatched. Then the asynchronous switched residual evaluation system is obtained, and global uniform exponential stability (GUES) and exponential H∞ performance of asynchronous switched system are guaranteed by using μ-dependent discontinuous multi-Lyapunov functions and MDADT method. The sufficient conditions for the existence of designed filter are given in terms of linear matrix inequalities (LMIs), and parameter matrices of the designed filter and MDADT can be obtained by solving these LMIs. Finally, the effectiveness of the proposed method is demonstrated by two examples.

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