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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。
The invariant set of discrete time-delay switched systems is constructed, and the design method of switching controller based on N-step invariant set is proposed. The range of the actuator’s non-linear attracting domain is estimated. First of all, considering the effect of time lag, the Lyapunov function which depends on time delay is chosen to construct the invariant set of the switched system with time-delay and to express it as the number of convex combinations and ellipsoidal sets of time-delay Constant related. Secondly, different saturation constraints are applied to the first N sampling points of the system to obtain a set of ellipsoid sets. The number of ellipsoid sets is related to the constant N, and the ellipsoid sets calculated in each step are time lags Switch the system’s invariant set. Then a set of N convex invariant sets is fitted with a set of convex hull coefficients to obtain a larger estimation of the attracting area. Finally, the switching law is designed under the condition of satisfying the average residence time constraint, and the state feedback controller is designed to ensure the closed-loop system is asymptotically stable. The Problem of Solving the Controller’s Conversion into Linear Matrix Inequalities. Simulation results verify the feasibility and effectiveness of the proposed method.