Robust Pole Assignment Via Dynamic Compensator In Descriptor Systems

The pole assignment for descriptor systems is a very important design in thecontrol systems, and has been studied widely. With the development and perfectionof the descriptor system, and thinking about the effect of irresistible interference onthe stability of the system in the real life, more and more people studied therobustness of the systems. In this paper, we make linear time-invariant descriptorsystem as the research object, and then study the robust pole assignment indescriptor system via dynamic compensator.Dynamic compensator feedback is the special form of output feedback. In thispaper, the systems we studied only have parts of parameter perturbations. First, weanalyse the pole assignment of the systems without considering perturbations. Thealgorithm of calculating the dynamic compensator feedback matrix is presented.Secondly, based on the dynamic compensator pole assignment result for descriptorlinear systems, we present a object function concerning the robustness. Suchfunction takes the affection of uncertainties to the closed-loop into consideration.And then according to the parametric solution, the parametric expression of theobject function is obtained, turning the pole assignment into the minimization ofeigenvalue sensitivity problem, computing the gradient of the objective function. Inthis, we only discuss the real condition, and present an explicit expression of thefunction. Finally, we give the numerical example indicates the algorithm of therobust pole assignment is easy and feasible, and improve the robustness of thesystems.