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研究了采用一个线性状态反馈控制器镇定多个线性奇异摄动系统的问题.同时镇定条件可以表达为一组矩阵不等式条件,所得条件与摄动参数无关,从而有效地回避了病态问题.采用基于快慢分解的两步法可以得到镇定控制器增益和相应的Lyapunov函数.而在每一步需要利用迭代线性矩阵不等式技术求解相应的双线性矩阵不等式,相关定理研究了算法的收敛性.本文所得结论可同时适用于标准与非标准奇异摄动系统.文末给出了相应的仿真算例.
The problem of using a linear state feedback controller to stabilize several linear singularly perturbed systems is studied. At the same time, the stabilization condition can be expressed as a set of matrix inequality conditions and the obtained conditions have nothing to do with the perturbation parameters, so the pathological problems are effectively avoided. The steady-state controller gain and the corresponding Lyapunov function can be obtained by the two-step decomposition method, and the iterative linear matrix inequality (LMI) technique is used to solve the corresponding bilinear matrix inequality at each step. The correlation theorem studies the convergence of the algorithm. It can be applied to both standard and non-standard singular perturbation systems. The corresponding simulation examples are given.