Robust stabilization of uncertain systems (Q1910066)

A controlled system with bounded deterministic uncertainty is described by a differential inclusion. Assuming that a Lyapunov function is known, a differential inclusion, governing the evolution of some subset of admissible controls in order to achieve asymptotic stability is derived. Under some regularity assumptions, a set-valued evolution law of stabilizing controls can be found explicitly. In order to implement a robust dynamical closed loop, a single valued explicit control scheme is proposed. An illustrative example is presented.