不确定双线性随机离散时间系统的鲁棒控制

Robust control of uncertain bilinear stochastic discrete-time systems

文章研究了不确定双线性随机离散时间系统的鲁棒控制。通过构造线性滤波,利用代数里卡提不等式与线性矩阵不等式(LMI)方法,使得系统状态均方有界,以及每个状态误差的协方差矩阵对角元素不超过对应预先设定的对称正定矩阵元素上确界,从而双线性随机系统可达到较好的鲁棒性。数值算例验证了该方法是有效的。

This paper focuses on the robust control of uncertain bilinear stochastic discrete-time systems.By constructing the linear filter and using the methods of algebraic Riccati inequality and linear matrix inequality（LMI）,the system is made be mean-square bounded,and the diagonal elements in the covariance matrix of the estimation error for each state are not more than the individual prescribed upper bound of the symmetric positive definite matrix elements.Therefore better robustness of the bilinear stochastic system can be achieved.A numerical example is provided to illustrate the effectiveness of the proposed design approach.