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针对奇异系统、双线性系统、时滞系统和不确定系统四方面结合的复杂系统进行了鲁棒控制研究。基于李雅普诺夫稳定性理论和线性矩阵不等式方法,此外还利用了集合域内放大的方法,对不确定项的参数是时变的但满足范数有界的奇异时滞的双线性系统,推导出其闭环系统鲁棒镇定的充分条件,给出了使得闭环系统鲁棒镇定的状态反馈控制器设计方法。定理基于LMI的方法解决了介于线性和非线性之间的一类不确定时滞奇异双线性系统的鲁棒控制问题,此方法设计的状态反馈控制器更加简单有效,使得系统能快速达到稳定状态。数值仿真说明了定理的合理性和有效性,为解决相关工程控制问题提供了一定理论依据。
The robust control of complex systems combining four singular systems, bilinear systems, time-delay systems and uncertain systems is studied. Based on the Lyapunov stability theory and the linear matrix inequality (LMI) method, the method of enlarging the ensemble domain is also used. The parameters of the uncertain term are time-varying bilinear systems that satisfy the singular lag with bounded norm. The sufficient conditions for the robust stabilization of the closed-loop system are given, and the state feedback controller design method for the robust stabilization of the closed-loop system is given. Theorem The LMI-based approach solves the robust control problem for a class of singular bilinear systems with time-delay and nonlinearity. The state feedback controller designed by this method is more simple and effective, stable state. The numerical simulation shows the rationality and validity of the theorem, which provides a theoretical basis for solving the engineering control problems.