Robust adaptive stabilization of time-invariant first-order hybrid systems with covariance resetting

This paper presents a robust adaptive stabilization scheme for a class of nominally controllable first-order hybrid time-invariant linear systems which involve both continuous and discrete signals. The usual assumptions of inverse stability of the plant and knowledge of the high-frequency gain are not required. The design philosophy used relies on the separation of the contributions to the output of the continuous and discrete dynamics through the generation of two additive signals to build the overall control action. The estimation scheme is unified in the sense that both continuous and discrete updated parameters are generated from the same adaptation error. The controllability of the nominally estimated plant model is maintained by using an hysteresis switching function under the controllability of the nominal plant. This allows relaxing the usual assumption of stability of the plant inverse. Also, an adaptation dead zone is used for robust stabilization by using a known overbounding function of the contribution of the unmodelled dynamics. (C) 1997 Elsevier Science Ltd.