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针对常数时滞线性系统的稳定性问题,基于一个适当形式的Lyapunov-Krasovskii泛函,通过利用一个积分不等式,采用时滞分解方法,以线性矩阵不等式的形式给出了时滞系统的时滞相关型稳定性准则。与现有的时滞相关型稳定性结果相比较,所得到的结果具有保守性更好,结构更加简单,且不含有任何多余的矩阵变量等特点,并从理论上进行了严格的证明,解决了现有的稳定性结果绝大多数只是从数值例子说明其有效性的问题。示例说明了所得结果的有效性。
Aiming at the stability of linear systems with constant time delay, based on an appropriate form of Lyapunov-Krasovskii functional, a delay-dependent system is proposed by using an integral inequality and a time-delay decomposition in the form of linear matrix inequalities Type Stability Criteria. Compared with the existing delay-dependent stability results, the obtained results are more conservative, simpler, and contain no extra matrix variables, and have been rigorously proved in theory Most of the existing stability results are only numerical examples to illustrate the validity of the problem. The example shows the validity of the results obtained.