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This paper presents and implements an iterative feedback design algorithm forstabilisation of discrete-time switched systems under arbitrary switchingregimes. The algorithm seeks state feedback gains so that the closed-loopswitching system admits a common quadratic Lyapunov function (CQLF) and henceis uniformly globally exponentially stable. Although the feedback designproblem considered can be solved directly via linear matrix inequalities(LMIs), direct application of LMIs for feedback design does not provideinformation on closed-loop system structure. In contrast, the feedback matricescomputed by the proposed algorithm assign closed-loop structure approximatingthat required to satisfy Lie-algebraic conditions that guarantee existence of aCQLF. The main contribution of the paper is to provide, for single-inputsystems, a numerical implementation of the algorithm based on iterativeapproximate common eigenvector assignment, and to establish cases where suchalgorithm is guaranteed to succeed. We include pseudocode and a few numericalexamples to illustrate advantages and limitations of the proposed technique.

Feedback stabilisation of switched systems via iterative approximate eigenvector assignment