Robust Stabilization of Uncertain Systems

In this paper we consider the systems described by \[dx = Axdt + Budt + ∑_i {σ _i F_i xdβ _i } {or} x = Ax + Bu + ∑_i {B_i F_i (x,t)C_i x,} \] and we will derive conditions under which there exists a feedback control law $u = Kx$ such that the closed loop system is stable for all σ ᵢ or (smooth) nonlinearities Fᵢ. The nonlinearities Fᵢ and the noisy gains σ ᵢ dβ ᵢ are unknown uncertainties in the system, and the problem considered is to obtain a control law which is robust against these uncertainties, as far as stability is concerned.