Poincaré maps modeling and local orbital stability analysis of discontinuous piecewise affine periodically driven systems

This paper presents a methodology to study the local stability of periodic orbits (orbital stability) in switched discontinuous piecewise affine (DPWA) periodically driven multiple-input multiple-output (MIMO) systems. The switched system of interest has a bilinear state space representation where the controller inputs are binary signals taking values in the set {0,1}. These systems are characterized by a set of affine differential equations together with switching rules to commute between them. These switching rules are described by switching functions that are periodic in time and linear in state. The methodology is based on obtaining a discrete time model (Poincaré map), its steady state operation points, and its Jacobian matrix. This provides a powerful tool for studying their stability and to predict some kind of instability phenomena that the system can undergo like subharmonic oscillations. The proposed approach is applied to a power electronic circuit which toggles among six different system equations with five switching boundaries within a switching cycle. This work was supported by the Spanish Ministerio de Educación y Ciencia under Grant TEC-2004-05608-C02-02.