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将美国密歇根大学的学者Bernstein教授和Hollot教授[1]提出的利用指数矩阵形式检测鲁棒稳定性的方法,推广到具有线性时不变(LTI)保持函数的采样控制系统中。直接使用了连续时间模型的原有数据,避免判断条件过于保守。构造了此类系统的标准Lyapunov函数的一个上限。此上限完全不依赖于系统原来的不确定参数,而只依赖于一个为了避免此上限过于保守而专门引入的一个自由标量参数。给出了一个可靠的数值计算的算法。并且将计算方法进行改进以进一步适用于具有任意广义采样保持函数(GSHF)的采样控制系统。
The method of exponential matrix detection of robust stability proposed by Professor Bernstein and Hollot [1] of the University of Michigan is extended to the sampling control system with linear time-invariant (LTI) preserving function. The direct use of the continuous data model of the original data, to avoid judging conditions are too conservative. An upper bound on the standard Lyapunov function that constructed such a system. This upper bound does not depend on the original uncertain parameters of the system, but only on a free scalar parameter specially introduced to avoid the upper bound being too conservative. A reliable numerical calculation algorithm is given. And the calculation method is improved to further apply to the sampling control system with arbitrary generalized sample and hold function (GSHF).