Robust Control of Time-Delay Uncertain Systems by Delay-Free Output Feedback

The problem of global stabilization by delay-free output feedback is considered for a class of time-delay nonlinear systems with uncertainty in both output and state equations. The nonlinear perturbations with time-delay in the state equation are allowed to satisfy a linear growth condition with a polynomial output-dependent rate, while the uncertain parameter in the system output is assumed to be located in a known compact set. By constructing appropriate Lyapunov-Krasovskii functionals, we present a recursive algorithm for the design of a delay-independent, estimator-based controller that consists of an estimator with a dynamic gain and an estimator-based feedback law, capable of dealing with simultaneously the uncertainty in the output and polynomial nonlinearities in the state dynamics.