ABSTRACT
Recently, the CLF method continues to be concerned by many researchers. A switched linear copositive Lyapunov function method for switched positive systems is presented in (Liu 2009), and the existence problem of a Common Copositive Lyapunov Function (CCLF) for switched positive linear systems with stable and pairwise commutable subsystems is investigated in (Tong et al. 2013). The present results demonstrated that a CCLF can be constructed for the underlying system whenever its subsystems are continuous time, discrete-time or the mixed type. Further, For the finite-time stability problem of switched positive linear systems, Chen and Yang present a sufficient condition for finite-time stability using the CCLF and multiple copositive Lyapunov functions (Chen & Yang 2014). Meanwhile a computational method for vector functions used to construct the CLF is proposed. A Common Diagonal Lyapunov Function (CDLF) is constructed for a special
1 INTRODUCTION
The stability of Switched Systems (SS) is a significant problem for practice. Many research works about it have been done since the early years. For example, the basic control analysis was carried out (Beldiman & Bushnell 1999). A Lie algebraic condition was proposed about the stability of SS (Liberzon & Morse 1999). The Lie-algebraic stability conditions for nonlinear switched systems subsequently were considered in (Margaliot & Liberzon 2006). Branicky showed solicitude for stability of SS in early years (Branicky 1994, Branicky 1997, Branicky 1998) and made excellent contribution to the field.
