Convex conditions for robust stabilization of uncertain switched systems with guaranteed minimum and mode-dependent dwell-time

Abstract

Alternative conditions for establishing dwell-time stability properties of linear switched systems are considered. Unlike the hybrid conditions derived in Geromel and Colaneri (2006), the considered ones are affine in the system matrices, allowing then for the consideration of uncertain switched systems with time-varying uncertainties. The low number of decision variables moreover permits to easily derive convex stabilization conditions using a specific class of state-feedback control laws. The resulting conditions are enforced using sum of squares programming which are shown to be less complex numerically that approaches based on piecewise linear functions or looped-functionals previously considered in the literature. The sums of squares conditions are also proven to (1) approximate arbitrarily well the conditions of Geromel and Colaneri (2006); and (2) be invariant with respect to time-scaling, emphasizing that the complexity of the approach does not depend on the size of the dwell-time. Several comparative examples illustrate the efficiency of the approach.