Modeling, Stability and Regulation for a Class of Dynamical Systems
by
Zvi Retchkiman Konigsberg
Centro de Investigacion en Computacion, I.P.N

This work describes the modeling, stability and regulation problem for a class of dynamical systems. The class of dynamical systems considered in this paper, are those that are positive and are characterized by the property that its trajectories experiment changes as a result of uniform (or non-uniform) switching inputs. In other words, the system of differential (or difference) equations that generate the positive trajectories are subjected to uniform (or non-uniform) switching inputs. As a consequence the trajectories may be (a) continuous or (b) piecewise continuous with a finite number of discontinuities, and jumps given by an arbitrary but fixed positive intenger number. The solution is achieved thanks to what is called dynamical coloured Petri nets (DCPN), and Lyapunov methods. Dynamical coloured Petri nets (DCPN) are an extension of coloured Petri nets and is the tool utilized to model the dynamical system under study. Once the model is obtained the stability and regulation problems are addressed. Assuming that the trajectories are bounded for the switching inputs, when they are fixed, stability for the switching times is guaranteed employing Lyapunov methods. Evenmore, regulation to some desired set point can be achieved by a proper selection of the switching inputs.

Date received: March 1, 2003