构造离散时滞切换系统的不变集,提出基于N步不变集的切换控制器设计方法,估计执行器饱和非线性的吸引域范围。首先,考虑时滞的影响,选取依赖于时滞的Lyapunov函数,构造时滞切换系统的不变集,并将其表达为若干个椭球集的凸组合,椭球集的个数与时滞常数相关。其次,在系统的前N个采样时刻,分别施加不同的饱和约束,求解得到一组椭球集,椭球集的个数与常数N相关,而每一步计算得到的椭球集均为时滞切换系统的不变集。再将N个不变集用一组凸包系数拟合,即可获取较大的吸引域估计。最后,在满足平均驻留时间约束的条件下设计切换律,并设计状态反馈控制器,保证闭环系统渐近稳定。控制器的求解转化为线性矩阵不等式的可行性问题。仿真结果验证了所提方法的可行性和有效性。
This paper deals with saturated control of a class of discrete-time linear switched systems with time delay. The switched controller design method is developed by using Nth-step invariant set and average dwell time approach. First, as time delay is considered, the Lyapunov function is chosen as delay-dependent. The invariant set of the switched systems with time delay is expressed as a convex combination of a set of ellipsoids, the number of which depends on a time delay constant. Second, some saturation constraints are given to obtain a set of ellipsoids at the first N sampling time, the number of which depends on N. The estimate of the domain of the attraction could be enlarged by assembling such ellipsoids with a convex combination. Finally, a state feedback controller and a permissible switching law, subject to the given average dwell time, can be obtained by solving a set of linear matrix inequalities. The feasibility and effectiveness of the proposed method are verified
