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

In this paper, new results are presented for H∞ 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∞ 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∞ performance, the corresponding H∞ 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.