Realization Theory for Discrete-Time Piecewise-Affine Hybrid Systems

The paper investigates the realization problem for piecewise-affine discrete-time hybrid systems. A piecewise-affine discrete-time hybrid system is a discrete-time system such that the state-transition and readout maps are piecewise-affine maps. We will restrict our attention to autonomous systems and we will study the following realization problem. For a specified output trajectory, find a piecewise-affine hybrid system which realizes this output trajectory. We will show that the realization problem for discrete-time piecewise-affine hybrid systems is equivalent to the realization problem for discrete-time switched linear systems. We will give necessary and sufficient conditions for existence of a realization by a discrete-time piecewise-affine and a discrete-time switched linear system. We will also present a procedure for constructing a discrete-time linear switched system and a discrete-time piecewise-affine hybrid system realizing the specified output trajectory.

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