Robust stability and stabilization of a class of uncertain nonlinear systems with delays

A class of nonlinear systems with norm-bounded uncertainties and state-delay is considered. Two criteria are developed for the robust stability analysis: one is delay-independent and the other is delay-dependent. Methods for robust feedback synthesis are then examined. It is established that linear memoryless controllers are capable of guaranteeing the delay-dependent and delay-independent stabilizability of the closed-loop systems. All the results are expressed in the form of linear matrix inequalities which can be solved by efficient and numerically-stable routines. The developed theory is applied to the stability robustness problem of an industrial jacketed continuous stirred tank reactor.