Feedback Controller Norm Optimization for Linear Time Invariant Descriptor Systems With Pole Region Constraint

An algorithm is proposed to compute a state feedback gain matrix for a linear time invariant, regular descriptor system, which ensures that i) the closed loop system is impulse-free and ii) all the finite poles are placed within a pre-defined stability region in the complex plane. The associated design flexibilities are exploited in minimizing upper bounds of the Frobenius norm of respective gain matrices. A class of linear matrix inequality (LMI) regions in the complex plane are chosen as constraints for the closed loop finite poles. By representing a subset of the nonsingular matrices through solution of an LMI, and linearizing the set of matrix inequalities, arise in the regional pole (finite poles) assignment, the associated optimizations are formulated as semidefinite programs. The effectiveness of the developed algorithm is demonstrated through numerical examples. Significant reduction in the norm of feedback gain matrix is achieved in a two generator six bus power system.