基于鲁棒稳定性的多速率采样控制系统设计

提出了基于鲁棒稳定性的多速率采样控制系统设计方法.对于具有给定补偿F的系统，首先拓展Lyapunov上限法得出鲁棒稳定性判定新条件.当系统具有边界不定的不确定性时，定义最大可承受边界为鲁棒稳定半径（Robust Stability Radius，RSR）.通过对鲁棒稳定判定条件的分析，可将求解RSR的问题归结为求解一个复杂非线性方程,并利用数值计算方法求解该方程得到解析解.作为F的函数，通过一般优化方法即可实现F优化设计，使得系统RSR最大，而且在保证鲁棒稳定的同时可以承受不确定参数的变化范围最大.最后给出实例，说明了所提方法的可行性和有效性.

Optimal Design of a Multirate Sampled-Data Control System Based on Robust Stability

This paper concerned the optimal design of a multirate sampled-data control system based on robust stability. For a system with a given F, a new condition for robust stability test of uncertain system was developed by extending Lyapunov upper bound method. For a system with an unknown uncertainty bound, the robust stability radius (RSR) was defined. The RSR calculation problem could be converted to a mathematical process of solving an equation by analyzing the robust stability test condition proposed. The equation was solved using numerical mathematical methods to get the analytical solution as RSR. As a function of F, the F optimization design could be achieved by a general optimization method to get the biggest RSR. With this F, the system could remain stable with the uncertain parameters varying set being the largest. Finally, a simple example was provided to test the feasibility of the proposed method.