Control of switched linear and affine systems

Abstract

This research project aims to study switched dynamical systems. These systems are composed by a finite number of subsystems and a rule that selects at each time instant one of them in order to assure stability and performance for the overall system. Actually, this proposal continues the researches I have made in the last years and it can be divided in three main parts. In the first, the goal is to study switched linear systems subject to time-delay by using, for example, Lyapunov-Krasovskii functionals. In the second, the goal is to treat switched systems subject to nonlinearities belonging to sectors known as Lur'e type switched systems. In this case, we want to generalize the well known Popov criterion to switched systems. The great challenge is to find a stability criterion based on the frequency domain to deal with switched systems that are time-varying and, therefore, do not have a frequency representation. The third part of this proposal aims to study switched affine systems that are more involved than the linear ones since they have several equilibrium points. In this case, the control goal in to determine not only the switching rule but also the set of attainable equilibrium points. The literature present only few results about this theme. Our proposal is to define H2 and Hoo performance criteria and to deal with state feedback control. Depending on the time and on the results we will obtain, the conditions will be generalized to cope with output feedback dynamical control. Finally, we want to apply the developed theory to deal with fault tolerant systems and the control through the communication network which are current themes of great practical interest. (AU)