Sufficient conditions for the genericity of feedback stabilisability of switching systems via Lie-algebraic solvability

Abstract

This paper addresses the stabilisation of discrete-time switching linear systems (DTSSs) with control inputs under arbitrary switching, based on the existence of a common quadratic Lyapunov function (CQLF). The authors have begun a line of work dealing with control design based on the Lie-algebraic solvability property. The present paper expands on earlier work by deriving sufficient conditions under which the closed-loop system can be caused to satisfy the Lie-algebraic solvability property generically, i.e. for almost every set of system parameters, furthermore admitting straightforward and efficient numerical implementation.

arXiv commentExtended version of that accepted at the XIV Workshop on Information Processing and Control (RPIC), Oro Verde, Entre Rios, Argentina, 2011