An iterative algorithm for the mixed H/sub 2//H/sub ∞/ control problem

Abstract

This paper is concemed with the mixed H z / H , control problem. The purpose of this paper is t o give an iterative method for obtainiig a sub-optimal solution. The obtained controller is the global optimal solution or a suboptimal solution on the boundary of H , constraint. The effectiveness of the proposed method is shown by a numerical example.

An iterative algorithm for the mixed H<inf>2</inf>/H<inf>∞</inf> control problem using H<inf>2</inf> norm decreasing controller sets

“…Lemma 1 [14] J(K) has the unique stationary point at K = K * 2 over all internally stabilizing controllers.…”

“…Then G i ≥Ĝ from Lemma 3-(i). On the other hand, G ≥ Z 2 (= G i ) for any G and K that satisfy (13) (see [14]). Hence, we have G i =Ĝ, which implies J(K *…”

“…Recently, multiobjective control problems have received a great deal of attention [1,2], [4]- [7], [9]- [14]. In particular, the socalled mixed H 2 /H ∞ control problem for linear time invariant (LTI) systems has been studied by many researchers.…”

“…Standard technique to get a sub-optimal solution is to use a common LMI solution at the expense of conservatism [2,4]. Recently, new methods using uncommon LMI solutions have been proposed [1], [9]- [14]. However, all of them except that in [14] do not show what kind of solutions are obtained, although it is important for sub-optimal methods to show the properties of the obtained solutions.…”