Measurement dynamic feedback output regulation in hybrid linear systems with state jumps

This work investigates the problem of designing a hybrid dynamic feedback regulator that forces the output of a hybrid linear system to asymptotically converge to the reference generated by a hybrid exogenous system, asymptotically rejects the exogenous disturbance, and attains global asymptotic stability of the compensated hybrid linear dynamics. The class of hybrid linear systems addressed exhibits a continuous-time linear behavior except at isolated points of the time axis, where the state is subject to discontinuities that are caused by a jump behavior. In the presence of possibly unequally spaced state jumps, under the only constraint that the minimum time between any two consecutive jumps is no smaller than a given positive real constant, both implicit and explicit sufficient conditions for the existence of a solution to the stated problem are shown. The explicit condition is constructive, in the sense that it outlines the algorithmic procedure for the synthesis of the hybrid feedback regulator, provided that a certain output-nulling hybrid controlled invariant subspace be known. Then, a necessary and sufficient condition for the existence of such subspace is proven, so that a computational means to derive it, if any exists, is given. Finally, the devised approach is applied to a numerical example borrowed from the literature, with the twofold aim of illustrating its implementation and making a comparison with the available method.