A generalized scaling based control design for nonlinear nontriangular systems with input and state time delays

A general class of nonlinear systems containing delays in both state and input is considered and a dynamic high-gain scaling based control design is proposed. The class of systems considered is of a general structure which is not necessarily of any triangular form. All functions appearing in the system dynamics are allowed to be uncertain as long as some polynomial bounds on ratios of uncertain system terms are available. Both state and input delays are allowed to be time-varying and uncertain. The control design is based on our recent results on generalized scaling utilizing appropriate (not necessarily successive) powers of the scaling parameter. The control implementation does not require knowledge of the time delays or any magnitude bounds thereof; the only information about the time delays that is required is a bound on the rate of variation of time delays.