Polyquadratic Stability of Positive Switched Systems with Time-Varying Polytopic Uncertainties via Structured Lyapunov Functions

Abstract

In this work we aim to propose new conditions for the polyquadratic stability of positive switched linear systems containing discrete-time varying polytopic uncertainties. Parameter Dependent Switched Structures Lyapunov Functions (PDSSLF) are used to obtain conditions that guarantee the polyquadratic stability and positivity of the dynamical system via Linear Matrix Inequalities (LMIs). The present work con-siders the case of discrete-time varying polytopic uncertainties in the switched state matrix. The switching function is of arbitrary type. The PDSSLF depends on both the switching function and the uncertainty parameter that describes the convex polytope of each mode of the switched system. The proposed conditions were evaluated on two example systems.