Supervised stabilisation of linear discrete-time systems with bounded variation rate

The stabilisation problem of linear, discrete-time, time-varying systems in the framework of the frozen-time approach is considered. Assuming bounded time variations of system parameters, a gain-scheduling control policy is proposed. A family of linear time-invariant eigenvalue assigning controllers is designed on the basis of the corresponding family of frozen-time plants. The final time-varying stabilising compensator is obtained defining a suitable event-driven switching logic among the elements of the controllers´ family. The purpose is to attain asymptotic stabilisation under relaxed conditions on the parameter variation rate and with a controller which is itself slowly varying in order to greatly reduce the online computational burden.