Continuous Robust Control Guaranteeing Functional Performance Index for Nonlinear Uncertain Systems

Robust control of uncertain dynamical systems is considered. A new class of continuous robust controllers is introduced not only to guarantee asymptotic or exponential stability but also to achieve certain performance measure with respect to the standard linear quadratic performance index or other classes of functional performance indices. The new analytical result on stabilisation and performance analysis of controlling nonlinear uncertain systems allows one to proceed robust control synthesis based on performance requirement on the system state and control energy, in a similar fashion as linear optimal control design with quadratic performance indices. The class of uncertain systems under consideration contains any uncertain system whose nominal system is uniformly asymptotically stable (or stabilisable). The uncertainties are assumed either to satisfy the matching conditions or the generalised matching conditions or to be of equivalently matched uncertainties. The required information about uncertain dynamics is merely that the uncertainties are bounded in Euclidean norm by a known function of the system state.