Positive realness and optimality problem for rectangular descriptor systems

The inverse linear quadratic optimal problem based on dynamic compensation for rectangular descriptor system is considered in this paper. First a dynamic compensator with a proper dynamic order is given such that the closed-loop system is admissible and extended strictly positive real (ESPR) in terms of Bilinear Matrix Inequality (BMI). In this case, a sufficient condition for the existence of the optimal solution is presented. Then the weight matrices of the linear quadratic performance index are derived to be a parameterized expression. In order to solve the inverse optimal control problem for the system, an algorithm to the minimization problem with the BMI constraints is proposed based on path-following algorithm, in which an optimal dynamic compensator and the weight matrices of the linear quadratic performance index can be obtained. Finally, a numerical example is provided to demonstrate the effectiveness and correctness of the proposed results.