Relaxed stabilization conditions for discrete-time 2-D T-S fuzzy systems

This paper focuses on the problem of further relaxing stabilization conditions for the Roesser type discrete-time 2-D T-S fuzzy system. A novel kind of non-PDC control scheme is proposed to stabilize the closed-loop 2-D T-S fuzzy system, and then less conservative stabilization conditions are developed by using a new non-quadratic Lyapunov function for the underlying 2-D T-S fuzzy system. For one fixed degree of the homogeneous polynomially parameter-dependent matrix, the conservatism could be further reduced by exploiting the algebraic property of fuzzy membership functions and the obtained stabilization conditions may asymptotically approach to exactness in a convergent sense. Moreover, there are no slack matrix variables introduced in the control synthesis, and hence the computational burden is less than the existing ones while the same or less conservative results could be obtained. A numerical example is also provided to illustrate the effectiveness of the proposed methods.