Regulator Theory for Switched Systems

The exact output tracking problem for systems with parameters’ 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 non-causal solutions. A major advantage, for the case of reference trajectory generated by a “switched” linear exosystem, is that a pure feedback solution is obtained. A linear map from the states of the exosystem to the desired system state is defined via a matrix differential equation whose constant solution provides asymptotic tracking, and coincides with the feedback law used in standard regulator theory. The obtained results are applied to a simple flexible structure with jumps in the pay-load mass.