Julio H. Braslavsky

Hernan Haimovich, Julio H. Braslavsky

This paper presents and implements an iterative feedback design algorithm for stabilisation of discrete-time switched systems under arbitrary switching regimes. The algorithm seeks state feedback gains so that the closed-loop switching system admits a common quadratic Lyapunov function (CQLF) and hence is uniformly globally exponentially stable. Although the feedback design problem considered can be solved directly via linear matrix inequalities (LMIs), direct application of LMIs for feedback design does not provide information on closed-loop system structure. In contrast, the feedback matrices computed by the proposed algorithm assign closed-loop structure approximating that required to satisfy Lie-algebraic conditions that guarantee existence of a CQLF. The main contribution of the paper is to provide, for single-input systems, a numerical implementation of the algorithm based on iterative approximate common eigenvector assignment, and to establish cases where such algorithm is guaranteed to succeed. We include pseudocode and a few numerical examples to illustrate advantages and limitations of the proposed technique.

Hernan Haimovich, Julio H. Braslavsky

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.