Delay-range-dependent robust BIBO stabilization of 2D discrete delayed systems via LMI approach

This paper focuses on delay-dependent bounded input bounded output (BIBO) stabilization of a class of two-dimensional (2D) discrete delayed systems described by Fornasini and Marchesini (FM) state-space models. The main contribution is to propose a linear matrix inequality (LMI) method to construct sufficient conditions on delay-range-dependent 2D BIBO stability, where the stability criterion guarantees that bounded input can lead to bounded output though the time delay has a direct effect on the system stability. To solve the problem, a novel relevant concept of 2D BIBO stability is first introduced. Then, the condition is formulated in terms of LMIS through the Lyapunov-Krasovskii function. Subsequently, the existence condition can be extended to the uncertain case. Meanwhile, the relation between BIBO stability and asymptotical stability is expatiated. The generality of the proposed design method is shown by results through constant delay case. Finally, an illustrative example of a causal 2D system is selected to demonstrate the effectiveness and merits of the proposed method. © IFAC