on the well-posedness, equivalency, and low-complexity translation techniques of discrete-time hybrid automaton and piecewise affine systems

The main contribution of this paper is to present the systematic and low-complexity translation techniques betweena class of hybrid systems referred to as automaton-based dha and piecewise affine (pwa) systems. as an startingpoint the general modeling framework of the automaton-based dha is represented which models the controlled anduncontrolled switching phenomena between linear continuous dynamics including discrete and continuous states,inputs and outputs. the basic theoretical definitions on the state trajectories of the proposed dha with forwardand backward evolutions which yield forward and backward piecewise affine (fpwa and bpwa) systems are given.next, the well-posedness and equivalency properties are proposed and the sufficient conditions under which the wellposedness property is achieved with the automaton-based dha and pwa systems are given. it is shown that thegraphical structure of the proposed automaton-based dha makes it possible to obtain analytically the equivalent pwasystem with a polynomial complexity in contrast to the existing numerical translation techniques via decomposedstructure of the dha with an exponential complexity. examples are presented to confirm the effectiveness of theproposed translation techniques.