Robust stabilization under structured, possibly unstable and impulsive uncertainties

Abstract

Necessary and sufficient conditions for the robust stabilization under structured dynamical uncertainties, which can be unstable and impulsive, are given. The order of the controller is predefined. It is shown that disturbances in some channels can be completely arbitrary, while the stability is preserved. It is shown that the solution to this problem can be applied to the fault-tolerant control, where the faults can be unstable and/or impulsive systems. The given conditions are expressed by nonconvex matrix inequalities. However, for two classes of systems, the conditions reduce to LMIs. Examples with random numbers illustrate the design algorithm.