Extended Lie Algebraic Stability Analysis for Switched Systems with Continuous-time and Discrete–time Subsystems
نویسندگان
چکیده
We 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.
منابع مشابه
Stability analysis of a class of switched linear systems on non-uniform time domains
This paper deals with the stability analysis of a class of switched linear systems on non-uniform time domains. The considered class consists of a set of linear continuous-time and linear discrete-time subsystems. First, some conditions are derived to guarantee the exponential stability of this class of systems on time scales with bounded graininess function when the subsystems are exponentiall...
متن کاملAnalysis of Discrete-Time Linear Switched Systems: A Variational Approach
A powerful approach for analyzing the stability of continuous–time switched systems is based on using tools from optimal control theory to characterize the “most unstable” switching law. This reduces the problem of determining stability under arbitrary switching to analyzing stability for the specific “most unstable” switching law. More generally, this so–called variational approach was success...
متن کاملStability Analysis and Controller Design of the Nonlinear Switched Systems via T-S Discrete-Time Fuzzy Model
esses etc, can be appropriately described by the switched model [3-8]. In this paper, we proposed an innovative representation modeling of the Takagi-Sugeno (T-S) fuzzy switched discrete-time system. The simulation of stability analysis methods based on Lyapunov stability theorem to study the stability and switching law design for the T-S fuzzy switched discrete-time systems. Sufficient conditi...
متن کاملSome Results on Practical Stabilizability of Discrete-Time Switched Systems
In this paper, we report some recent development on practical stabilizability of discrete-time switched systems. We first introduce some practical stabilizability notions for discrete-time switched systems. Then we propose some sufficient conditions for the -practical asymptotic stabilizability of such systems. Furthermore, we focus on a class of discrete-time switched systems — namely, switche...
متن کاملOn robust Lie-algebraic stability conditions for switched linear systems
This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novel feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system paramete...
متن کامل