Algorithm For Robust Pole Assignment

This paper considers robust pole assignment in linear systems via state feedback. Based on the condition number of eignvector matrix and its full parameterztion, the parametric formula of index funtion for robust pole assignment is proposed, and then the explicit gradient formula of index function about design parameters is established. By using this explicit gradient formula and three optimization methods: Quasi-Newton method, conjugate-gradient method, Newton method, a very simple and efficient algorithm for robust pole assignment in linear systms via state feedback is presented. To avoid singularity in the algorithm, some parameters are fixed properly: 1 or n . The case that the design parameters are free is also considered in the paper. According to different numbers of the parameters fixed, different results are obtained. Because of the explicit gradient in the algorithm, we may establish a very rigorous stooping criteria and rapid local convergence.Because only the first-derivative is used in Quasi-Newton algorithm, the memorizing storage is low. Beside, properly chosing adjusted formula may reduce the value of the index function. Since conjugate-gradient method chose proper search direction, it improves the convergence very much. Several examples are discussed by using quasi-Newton method and conjugate-gradient method in the paper.