Control synthesis of Roesser type discrete-time 2-D T–S fuzzy systems via a multi-instant fuzzy state-feedback control scheme

This paper is concerned with further relaxations for control synthesis of the Roesser type discrete-time 2-D T–S fuzzy systems. A novel multi-instant fuzzy state-feedback control scheme and a new multi-instant Lyapunov function, which are homogeneous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions along two independent directions, are developed to stabilize the underlying 2-D T–S fuzzy system with less conservatism. Because more useful information about both current-time and past-time normalized fuzzy weighting functions is involved into control synthesis, the relaxation quality of control synthesis could be improved significantly. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.