scholarly journals Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time Subsystems

2007 ◽  
Vol 17 (4) ◽  
pp. 447-454 ◽  
Author(s):  
Guisheng Zhai ◽  
Xuping Xu ◽  
Hai Lin ◽  
Derong Liu
Keyword(s):  
Stability Analysis ◽  
Lie Algebra ◽  
Discrete Time ◽  
Continuous Time ◽  
Switched Systems ◽  
Switched System ◽  
Quadratic Lyapunov Function ◽  
Algebraic Stability ◽  
Arbitrary Switching ◽  
Exponentially Stable

Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-Time and Discrete-Time SubsystemsWe analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.

scholarly journals Analysis of Iterative Learning Control for a Class of Linear Discrete-Time Switched Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Xuan Yang ◽  
Xiaoe Ruan
Keyword(s):  
Discrete Time ◽  
Switched Systems ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
Switched System ◽  
Time Interval ◽  
Bounded Noise ◽  
Arbitrary Switching ◽  
Control Scheme

An iterative learning control scheme is applied to a class of linear discrete-time switched systems with arbitrary switching rules. The application is based on the assumption that the switched system repetitively operates over a finite time interval. By taking advantage of the super vector approach, convergence is discussed when noise is free and robustness is analyzed when the controlled system is disturbed by bounded noise. The analytical results manifest that the iterative learning control algorithm is feasible and effective for the linear switched system. To support the theoretical analysis, numerical simulations are made.

The Stability Analysis and Controllers Design with Packet Dropouts for Discrete-Time NCSs Based on Augmented Switched System

2014 ◽  
Vol 651-653 ◽  
pp. 980-983
Author(s):  
Dan Li Wen ◽  
Huai Yong Deng
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
State Feedback ◽  
Switched System ◽  
Packet Dropouts ◽  
The Stability

This paper was concerned with stability analysis and controlers design with packet dropouts for discrete-time NCSs. Stability controllers via state feedback is constructed for the switched system by using an LMI-based method.

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