基于饱和关联Lyapunov函数的饱和离散系统吸引域估计

Improved Estimation of Domain of Attraction of Discrete-Time Systems with Actuator Saturation by a Saturation-Dependent Lyapunov Function

考虑执行器饱和的线性离散时间系统的吸引域估计问题,基于饱和关联的Lyapunov函数的吸引域估计,较之二次Lyapunov函数具有明显的优势,但这些结果仍具有一定的保守性。针对这一问题,提出了改进的局部稳定性条件,同时给出求解最大吸引域估计的优化问题。改进的稳定性条件含有更多的未知变量,已有结果是其一种特例。仿真算例验证了文中所得结论的正确性和优越性。

In this paper, the problem about the estimation of domain of attraction for discrete-time linear systems subject to actuator saturation is considered. It is known that the results by saturation-dependent Lyapunov functions are better than that by quadratic Lyapunov functions. However, the results also have some conservativeness. For this, we propose an improved stability conditions, and also give the optimization solutions for the largest estimation of domain of attraction. It is noting that our improved conditions have more variables, and generalizes the existing results. At last, a simulation example is presented to show the effectiveness of our results.