Robust adaptive regulation of potentially inversely unstable first-order hybrid systems

This paper presents a robust adaptive stabilization scheme for a class of hybrid time-invariant linear system involving both continuous and discrete signals. The continuous subsystem and the discrete one are both of first-order. The usual assumptions of inverse stability of the plant and knowledge of the high-frequency gain are not required for this first-order hybrid system. The design philosophy used relies on the separation of the continuous and discrete dynamics by generating two additive terms to build the control action. The estimation scheme is unified in the sense that both continuous and discrete estimated 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.