Optimal control with regional pole constraints: an algebraic matrix equation approach

The design of optimal state feedback controller of linear time invariant systems with algebraic regional pole constraint is studied. The design method is based on optimal control theory and algebraic matrix equations, which are constructed according to the boundary of the constraint region. The constraint region may be determined by several algebraic inequalities, so it can approach the desired region very closely. The necessary and sufficient conditions for the optimal state feedback control law that shall ensure all closed-loop system poles lie within the constraint region and, meanwhile, shall minimize a multi-objective performance index, is derived. The performance index is consisted of two parts, namely, one part is used to penalize the sustained error, while the other part is used to guarantee that the closed-loop poles shall lie within the desired region and to improve the robustness properties of the closed-loop system.<>