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This paper defines a new class of hybrid systems called piecewise polynomial (PWP) systems in strict form and develops a backstepping controller synthesis methodology for these systems. The main contribution of the paper is to formulate controller design for a large class of PWP systems as a convex feasibility problem. The controller synthesis problem for PWP systems in strict feedback form is divided...
The first important contribution of this paper is to introduce for the first time a duality-based interpretation of piecewise affine (PWA) systems. This enables PWA controller synthesis to be formulated as a convex optimization problem. PWA L2-gain analysis and synthesis is also extended to PWA systems whose output is also a PWA function of the state (as opposed to a piecewise-linear function). In...
This paper addresses backstepping controller synthesis for piecewise affine (PWA) systems. The main contribution of the paper is to formulate controller design for a large class of PWA systems as a convex problem. Integrator backstepping is proposed as the principal design step in constructing Lyapunov functions for PWA systems in strict feedback form. The controller synthesis problem is divided into...
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