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 pie...

This paper considers a limit cycle control problem of a multi-modal and 2-dimensional piecewise affine control system. Limit cycle control means a controller design method to generate a limit cycle for given piecewise affine control systems. First, we deal with a limit cycle synthesis problem and derive a new solution of the problem. In addition, theoretical analysis on the rotational direction...

Piecewise affine systems are systems with a piecewise defined state equation. The continuous dynamics of these systems are affine but switch at the boundaries of certain subsets of the state-space. At these boundaries sliding modes may occur. A method will be presented to obtain a discrete-time system from a given continuous-time piecewise affine system. This method takes into account sliding m...

The paper addresses the realization and identification problem for a subclass of piecewise-affine hybrid systems. The paper provides necessary and sufficient conditions for existence of a realization by a piecewise-affine hybrid system. The paper also proposes an identification algorithm for this subclass of hybrid systems. The considered system class and the identification problem are motivate...

In this paper we consider three-tank system as a hybrid system with discrete (on/off) valves and then we use Hybrid System’s Description Language to acquire a Mixed Logical Dynamical model of the system. In order to obtain a relatively accurate model of three-tank system, instead of using straight line approximation method for linearization of valves in whole space, we use Piecewise Affine meth...

This paper is devoted to development of a new synthesis method of a multi-modal and 2-dimensional piecewise affine system that generates a desired stable limit cycle and investigation of some characteristics for the system. The new proposed method has some advantages on the convergence property of solution trajectories to a desired limit cycle in comparison with the previous one. First, the pro...