Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 63, pp. 1-19.

Title: Stability of simultaneously triangularizable switched systems 
       on hybrid domains

Authors: Geoffrey Eisenbarth (Baylor Univ., Waco, TX, USA)
         John M. Davis       (Baylor Univ., Waco, TX, USA)
         Ian Gravagne        (Baylor Univ., Waco, TX, USA)

Abstract:
 In this paper, we extend the results of [8, 15, 22],  
 which provide sufficient conditions for the global exponential stability 
 of switched systems under arbitrary switching via the existence of a 
 common quadratic Lyapunov function. In particular, we extend the Lie 
 algebraic results in [15] to switched systems with hybrid 
 non-uniform discrete and continuous domains, a direct unifying 
 generalization of switched systems on R and Z, 
 and extend the results in [8, 22] to a larger class 
 of switched systems, namely those whose subsystem matrices are 
 simultaneously triangularizable. In addition, we explore 
 an easily checkable characterization of our required hypotheses 
 for the theorems. Finally, conditions are provided under which 
 there exists a stabilizing switching pattern for a collection of 
 (not necessarily stable) linear systems that are simultaneously 
 triangularizable and separate criteria are formed which imply 
 the stability of the system under a given switching pattern 
 given a priori.

Submitted September 13, 2013. Published March 05, 2014.
Math Subject Classifications: 93C30, 93D05, 93D30.
Key Words: Switched system; common quadratic Lyapunov function;
           simultaneously triangularizable; hybrid system; time scales.