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Amir Ali Ahmadi(a_a_aprinceton.edu) Abstract: We introduce the concept of sosconvex Lyapunov functions for stability analysis of both linear and nonlinear difference inclusions (also known as discretetime switched systems). These are polynomial Lyapunov functions that have an algebraic certificate of convexity and that can be efficiently found via semidefinite programming. We prove that sosconvex Lyapunov functions are universal (i.e., necessary and sufficient) for stability analysis of switched linear systems. We show via an explicit example however that the minimum degree of a convex polynomial Lyapunov function can be arbitrarily higher than a nonconvex polynomial Lyapunov function. In the case of switched nonlinear systems, we prove that existence of a common nonconvex Lyapunov function does not imply stability, but existence of a common convex Lyapunov function does. We then provide a semidefinite programmingbased procedure for computing a fulldimensional subset of the region of attraction of equilibrium points of switched polynomial systems, under the condition that their linearization be stable. We conclude by showing that our semidefinite program can be extended to search for Lyapunov functions that are pointwise maxima of sosconvex polynomials. Keywords: Difference inclusions, switched systems, nonlinear dynamics, convex Lyapunov functions, algebraic methods in optimization, semidefinite programming. Category 1: Applications  Science and Engineering (Control Applications ) Category 2: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Category 3: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: Download: [PDF] Entry Submitted: 03/06/2018 Modify/Update this entry  
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