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考虑一类由局部状态空间Fornasini-Marchesini(FM LSS)第二模型描述的,具有时变状态滞后非线性二维(2-D)离散系统的稳定性分析和控制问题.时变状态滞后项的上、下界为正整数,非线性项满足Lipschitz条件.首先,通过引入一个含有时滞上、下界的新Lyapunov函数,给出了系统的稳定性准则;然后设计了状态反馈控制器以保证系统的稳定性,进而,状态反馈控制律可由线性矩阵不等式求得;最后通过数值算例表明了所得结果的有效性.
Consider a class of stability analysis and control problems for a two-dimensional (2-D) discrete-time system with time-varying state delay as described by the Fornasini-Marchesini (FM LSS) second model. The upper and lower bounds are positive integers, and the nonlinear terms satisfy the Lipschitz condition. First, by introducing a new Lyapunov function with upper and lower bounds on the delay, the stability criterion of the system is given. Then the state feedback controller is designed to ensure that the system Stability, and then, the state feedback control law can be obtained by the linear matrix inequality; Finally, numerical examples show the validity of the results obtained.