基于多输入时滞脉冲模型的采样数据控制系统的随机镇定

Stochastic stabilization of sampled-data control systems based on impulsive model with multiple input delays

针对具有非均匀采样的采样数据控制系统,把区间内连续分布的采样间隔序列描述为多元独立同分布随机过程,把闭环系统转化为多输入时滞脉冲模型,通过构造合适的非连续Lyapunov泛函,以及合理地利用在所有采样间隔内输入时滞的时间导数等于1的条件,结合自由权矩阵方法推导了基于LMIs的全局均方渐近稳定性条件,在此基础上运用调节因子法和锥补线性化方法,把控制器设计转化为具有LMI约束的非线性优化问题,并给出了基于LMIs的迭代求解算法.数值实例和实验表明了所得理论结果的优越性和有效性.

For a sampled-data control system with nonuniform sampling, the sampling interval sequence, which is distributed in an interval, is described as a multiple independent identically distributed process. The closed-loop system is transformed into an impulsive model with multiple input delays. By creating an appropriate discontinuous Lyapunov functional and rationally exploiting the condition that the derivative of input delay equals 1 in all sampling intervals, we derive a LMIs-based global mean-square asymptotical stability criterion based on free weight matrix approach. By using regulatory factor technique and cone-complementary linearization method, we transform the controller design method to a nonlinear optimization problem with LMI constraints, and an LMI-based iterative solution algorithm is given. Numerical examples and experimental results demonstrate the advantages and effectiveness of our theoretic results.