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研究一类具有区间时变输入时滞与状态时滞线性系统的稳定性问题.通过选择合理的Lyapunov-Krasovskii函数,基于积分等式方法(积分等式由自由权矩阵构造而成),以LMI的形式给出时滞相关的稳定性充分条件,并进行了相关控制器的设计.所得结论对时滞导数没有任何限制,可用于快时变时滞系统.同时,积分等式方法较积分不等式方法更优,保守性更低.最后,通过数值比较及仿真表明了所提出方法的有效性和优越性.
The stability of a class of linear systems with time-varying input delay and state delay is studied. By choosing reasonable Lyapunov-Krasovskii function and integrating integral equation (the integral equation is constructed by the free-weight matrix), the LMI , The sufficient conditions for the stability of the delay-dependent system are given and the design of the controller is carried out. The conclusion does not have any restrictions on the derivative of the delay and can be used in the time-varying delay system. Meanwhile, the integral equation method is better than the integral inequality The method is better and the conservative is lower.Finally, the effectiveness and superiority of the proposed method are demonstrated by numerical comparison and simulation.