Direct Piecewise Affine Systems: A New Class of Hybrid Systems with Affine Dynamics and Regulable Switching Boundaries

For many applications, Piece-Wise Affine (PWA) systems are made from approximation of nonlinear dynamics by affine subsystems. Approximation and non-exact stability analysis are the main disadvantages of derived PWA system and as a solution, a new class of hybrid systems are introduced in this article. The proposed class is derived directly from switched model and without averaging then it is named as Direct PWA (DPWA). The new hybrid class has affine subsystems and regulable and/or constant switching boundaries. Many applications such as power electronics and process engineeringcan be modeled as proposed class. Some theorems are presented for stability analysis that are based on quadratic Lyapunov function. The problem of stability analysis and controller design is redounded to convex optimization in form of linear matrix inequality. The proposed model is compared with conventional hybrid models. Proposed model is used for modeling and stability analysis of a dc-dc resonant power converter.