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基于齐次多项式Lyapunov函数这一新工具研究了时变不确定系统鲁棒稳定性问题.针对常见的含参数时变且有界连续可微线性系统的最大稳定区域问题,首先构造常用的参数依赖二次Lyapunov函数,进而给出一个时变系统稳定的充分条件.然后,通过构造适合的参数依赖齐次Lyapunov函数,并利用齐次多项式矩阵表示方法,最终以线性不等式的形式给出系统全局渐近稳定的一个充分条件.数值仿真结果表明齐次Lyapunov函数方法得到的结论对于某些系统比之前类似文献具有更小的保守性.
Based on the new tool of homogeneous polynomial Lyapunov function, the problem of robust stability of time-varying uncertain systems is studied. For the problem of the most stable regions of time-varying and bounded continuous differentiable linear systems with time-varying parameters, firstly, the commonly used parameter dependence Quadratic Lyapunov function, then a sufficient condition for the stability of a time-varying system is given.Finally, by constructing the suitable parameters relying on homogeneous Lyapunov functions and using the method of homogeneous polynomial matrix representation, we give the system global in the form of linear inequalities A sufficient and nearly sufficient condition is obtained. The numerical simulation results show that the conclusion obtained by the homogeneous Lyapunov function method is less conservative for some systems than the previous similar literature.