Input-output transition models for discrete-time switched linear and nonlinear systems

Abstract

Switched systems (such as those suitably representing next-generation communication networks, advanced embedded systems, chemical process control systems, networked power systems, teams of autonomous agents, etc.) are usually represented in state space form, as state space models give a more complete description of the system dynamics. In practice, however, we often make use of input-output models for identification and control purposes. Vast literature acknowledges that if we have one input-output model corresponding to each subsystem of the switched system, then at the switching instants, none of these input-output models can properly describe the system behaviour. Although the above problem is known to exist, there are very few effective and readily usable results (to our best knowledge) that exists in the open literature on the explicit form of the input-output models at the switching instants. In this paper, we rigorously develop a rather simple, yet effective, procedure to derive the input-output models from switching state space models. We call the additional input-output models during switching as the "transition models." We further rigorously prove that the models are invariant to coordinate transformations of the states. The advantage of our approach is its relative simplicity (and thus an easily adoptable methodology), and its ready applicability for the typically more difficult classes of switched nonlinear systems and MIMO systems. Simulations show that utilizing these transition models improves the performance of the controllers and identification of switched systems significantly.