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The Structure of Common Linear Copositive Lyapunov Functions for Continuous time Switched Positive Linear Systems

Zhu Liqin and Wu Zhaorong
School of Mathematical Sciences, University of Jinan, Jinan, China
Abstract—This paper addressed the structure of common linear copositive Lyapunov function (CLCLFs) for continuoustime switched positive linear systimes (CSPLS). In this note, first of all, for the n×n-dimensinal matrices family, which entries are the Hurwitz and Metzler switch matrices of an n-dimensional CSPLS, we presented, by a straightforward algebraic computation, a procedure for constructing a group n-dimensional vectors, further, we provided a structure theorem of CLCLFs, which shown that all CLCLFs of a CSPLS make a positive open cone generated by these special selected vectors, finally, an numerical example is worked out to illustrate our main results. The results of this technical note are extensions of some recent results in Ref. [1].

Index Terms—positive switched system, common linear copositive Lyapunove function, structure

Cite: Zhu Liqin and Wu Zhaorong, "The Structure of Common Linear Copositive Lyapunov Functions for Continuous time Switched Positive Linear Systems," Jounal of Automation and Control Engineering, Vol. 2, No. 2, pp. 187-190 June, 2014. doi: 10.12720/joace.2.2.187-190
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