Robust Pole Assignment Based On Mixed Sensitivity Index In Descriptor System

Descriptor system is a kind of dynamic systems of more general and abroad applied background, and has attracted much attention in the last three decades. This dissertation focuses on the linear time-invariant descriptor systems. It addresses the problem of robust state-feedback pole assignment in descriptor linear systems. There are two types of methods for solving the problem of robust pole assignment: one considers the problem of closed-loop system eigenvalue sensitivity to small parameter variations in some, but not all, of the elements of the open-loop system matrices; the other considers the problem of closed-loop system eigenvalue sensitivity to parameter variations in all of the elements of the open-loop system matrices. The former is more practical significant because most of the practical systems often possess special forms and structure information about system parameter perturbations is usually known.In this dissertation the problem of robust state-feedback pole assignment in linear systems with parameter perturbations in some of the elements of the open-loop system matrices is investigated. Firstly, a new object function concerning the robustness of the closed-loop is given. Such objective function takes quantificationally the effect of uncertainties to the closed-loop into consideration. Secondly, based on the eigenstructure assignment result for descriptor linear systems, the parametric expression of the optimization index is obtained. For real closed-loop eigenvalues and complex-conjugate closed-loop eigenvalues, an explicit gradient formula of the index function is established, then a simple and effective algorithm is proposed. Finally, an example is worked out to show that robust pole assignment algorithm proposed in the dissertation is simple and effective, and gives control systems with better robustness.