Passivity Analysis and Passification of Discrete-Time Hybrid Systems

Abstract

For discrete-time hybrid systems in piecewise affine or piece-wise polynomial (PWP) form, this note proposes sufficient passivity analysis and synthesis criteria based on the computation of piecewise quadratic or PWP storage functions. By exploiting linear matrix inequality techniques and sum of squares decomposition methods, passivity analysis and synthesis of passifying controllers can be carried out through standard semidefinite programming packages, providing a tool particularly important for stability of interconnected heterogeneous dynamical systems.