时变时滞复杂动态网络的非脆弱性同步保性能控制

Non-fragile synchronous guaranteed cost control for complex dynamic network with time-varying delay

针对一类时变时滞复杂网络系统,提出了一种非脆弱性同步保性能控制方法。在假设非线性向量函数f(x)可微条件下,通过Jacobi矩阵方法进行线性化处理,余项满足匹配条件,设计具有增益摄动的非脆弱性状态反馈控制器,以确保当控制器的参数发生小的摄动时,仍能保证控制器的有效性。通过构造合适的Lyapunov-Krasovskii泛函,采用积分等式、矩阵分析、Schur补定理等方法,在给定的保性能指标的条件下,得到了该系统非脆弱性同步保性能控制存在的充分条件;并证明了该条件等价于一组线性矩阵不等式(LMI)的可行性问题,给出了LMI约束条件下的凸优解构造方法,求出了闭环时变时滞系统保性能值的最小值。最后,通过数值算例对比验证了设计方法的可行性。

A kind of non-fragile synchronization guaranteed cost control method was put forward for a class of time-varying delay complex network system. Under the condition of assuming that the nonlinear vector functionf（x） was differentiable, a non-fragile state feedback controller with gaining perturbations was designed through the method of Jacohi matrix linearization with remainder satisfying matching conditions, to ensure that the parameters of controller could still be effective under small perturbation. The sufficient conditions for the existence of non-fragile synchronous guaranteed cost control of this system were obtained by constructing suitable Lyapunov-Krasovskii functional, using integral equation, matrix analysis, theorem of Sehur complement and so on. Under the condition of a given insurance performance index, the condition which was equivalent to the feasibility of a set of Linear Matrix Inequality （LMI） problem was shown, and the convex optimization construction method under the condition of LMI constraints was given, and the minimum value of the closed-loop time-varying delay system guaranteed performance value was calculated. Finally, by a numerical example comparison, the feasibility of the design method was verified.