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研究了一种新颖时滞模型:随机双曲正切模型的鲁棒H∞控制问题,模型的状态空间是由双曲正切函数表示的。利用状态的双曲正切函数设计出一种静态反馈控制器,它可保证相应的闭环系统均方渐近稳定而且可达到给定的H∞性能指标。利用Lypunov-Krasovskii和自由权矩阵方法,导出了由线性矩阵不等式表示的保证存在期望的控制器的时滞依赖的稳定性准则。利用计算机Matlab软件给出了一个仿真例子用以说明给出的方法的有效性。
A novel time-delay model is studied: Robust H∞ control problem for stochastic hyperbolic model, the state space of the model is represented by hyperbolic tangent function. A hyperbolic tangent function is used to design a static feedback controller, which guarantees the asymptotically stable mean square of the corresponding closed - loop system and achieves the given H∞ performance index. Using the Lypunov-Krasovskii and the free-weight matrix method, we derive the stability criterion that guarantees the existence of the expected delay-dependent controller by the linear matrix inequality. Using computer Matlab software gives a simulation example to illustrate the effectiveness of the given method.