A supervised switching technique for the robust stabilization of a class of linear discrete-time time-varying systems

The stabilization problem of a class of linear, discrete-time, time-varying, uncertain systems is considered. The elements of the dynamical matrix A(.) of a given time-varying system are modelled as unknown time functions taking values inside known compact sets. The elements of A(.) are varying inside a fixed set for a sufficiently long time interval, and, at some unknown time instants, they suddenly switch from the actual set to another one. The measure and the control matrices of the system are assumed to be known and time-invariant. It is required to find a dynamic output controller yielding an asymptotically internally stable closed-loop system. The solution proposed is given by the connection of a family of linear controllers with a supervised switching scheme.