Regulator theory for switched systems

In this paper the exact output tracking problem for systems with parameter jumps is considered. Necessary and sufficient conditions are derived for the elimination of switching-introduced output transient. Previous works have studied this problem for minimum-phase systems. In contrast, our approach, which is also applicable for nonminimum-phase systems, obtains bounded but possibly noncausal solutions. A major advantage, when reference trajectories are generated by an exosystem, is that a feedback-control based solution is obtained. As in standard regulator theory, we obtain a linear map from the states of the exosystem to the desired system state which is defined via a matrix differential equation. The constant solution of this differential equation provides asymptotic tracking, and coincides with the feedback law used in standard regulator theory. The obtained results are applied to a simple flexible manipulator with jumps in the pay-load mass.