Improved H∞ control of discrete-time fuzzy systems:: a cone complementarity linearization approach

In this paper, new results are presented for H-infinity analysis and synthesis problems of discrete-time Takagi-Sugeno (TS) fuzzy systems. By defining a multiple Lyapunov function, a new sufficient condition guaranteeing the H-infinity performance of the TS fuzzy systems is first derived, which is expressed by a set of linear matrix inequalities (LMIs). Both theoretical analysis and numerical examples show that such a new condition is less conservative than previous results obtained within the quadratic framework. Based on this new condition for H-infinity performance, the corresponding H-infinity controller design problem is then investigated. Different from the traditional quadratic framework, the synthesis problem is solved by exploiting the cone complementarity linearization (CCL) method, together with a sequential minimization problem subject to LMI constraints obtained for the existence of admissible controllers, which can be readily solved by using standard numerical software. (c) 2004 Elsevier Inc. All rights reserved.