Invariance of a class of semi-algebraic sets for polynomial systems with dynamic compensators

Abstract We derive a constructive sufficient condition for the existence of a compensator such that a prescribed semi-algebraic set is invariant for the resulting closed-loop system. The construction procedure consists of symbolic computations. Although the target system is restricted to polynomial control systems, non-polynomial smooth compensators can be designed. We also derive the procedure for extracting static controllers from the set of dynamic compensators. Moreover, we explain the similarities and differences between our method and the conventional slack-variable method of Jacobson and Lele (1969).