CONTROLLER APPROXIMATION WITH SOME PERFORMANCE VIA LINEAR MATRIX INEQUALITIES

摘要

This paper studies the problems of suboptimal H{sub}∞ controller approximation and extended strictly positive real controller approximation. The sufficient and necessary conditions for existences of the reduced order controller are obtained thatinvolve a several of LMIS and rank constraint condition of matrix. Moreover the parameterization of reduced order controllers is obtained. Therefore the free parameter can be selected such that the reduced order controller or the closed-loop systemsatisfy some other performances. LMIS can be solved by convex optimization method. But the rank constraint condition is nonconvex. The alternating projection method and semi-definite programming can be used to solve LMIS with rank constraint conditionnumerically. However this problem still need to be studied furthermore from theory to algorithm.