Stability criteria for feedback-controlled, imperfectly known, bilinear systems with time-varying delay

Abstract

The problem of synthesizing a class of continuous, memoryless feedback controls in order to stabilize a class of imperfectly known homogeneous-in-the-state bilinear time-delay systems is considered. In particular, bilinear systems with state time-delay in the linear term are investigated. The time-delay is assumed to be an unknown time-varying function with known upper bound on its derivative. As well as considering both matched and residual uncertainty, the uncertainty in the class of systems can be state, delayed-state and input dependent, and time-varying. Prior information on the bound of the system uncertainty is required; such bounding information allows for quadratic growth with respect to the state. For this stabilizability problem, a stability criterion, involving the upper bound on the derivative of the time-varying time-delay is obtained.