Abstract:
This article is concerned with uniform exponential stability, under arbitrary switching, in discrete-time switched positive linear systems with rank-one modes. Two differ...Show MoreMetadata
Abstract:
This article is concerned with uniform exponential stability, under arbitrary switching, in discrete-time switched positive linear systems with rank-one modes. Two different, but equivalent, novel necessary and sufficient conditions for uniform exponential stability in switched systems of this class are presented and proved in the paper. A switched positive linear system with rank-one modes is proved to be uniformly exponentially stable if and only if the spectral radii of an specific finite set of matrices associated to the system are smaller than one. It is also proved that the uniform exponential stability of a switched positive linear system with rank-one modes is equivalent to the feasibility of specific sets of linear inequalities associated to the system; thus allowing for a computationally efficient uniform exponential stability determination in this class of switched systems. This last result is furthermore a constructive converse Lyapunov theorem; establishing that each feasible solution to the aforementioned linear inequalities yields to (or generates) a common Lyapunov function, for the switched system, which is represented by as many linear functionals as modes the switched system has. An example is included that illustrates the results reported in the paper.
Published in: 2016 American Control Conference (ACC)
Date of Conference: 06-08 July 2016
Date Added to IEEE Xplore: 01 August 2016
ISBN Information:
Electronic ISSN: 2378-5861