Piecewise generalised H2 controller synthesis of discrete-time fuzzy systems

A generalised H₂ controller synthesis method for discrete-time fuzzy systems based on a piecewise Lyapunov function is presented. The basic idea of the proposed approach is to construct a controller for the discrete-time fuzzy systems in such a way that a piecewise Lyapunov function can be used to establish global stability with generalised H₂ performance for the resulting closed-loop fuzzy control systems. It is shown that the control laws can be obtained by solving a set of linear matrix inequalities that are numerically tractable with commercially available software. An example is presented to demonstrate the advantage of the proposed approach.