执行器饱和的分段齐次Markov跳变系统的镇定

研究一类带有执行器饱和的Markov跳变系统的镇定问题,转移概率是分段齐次的.首先,通过建立合适的Lyapunov泛函,运用椭球不变集估计系统均方意义的吸引域,得到由线性矩阵不等式约束的闭环系统随机稳定的充分条件.然后,通过求解凸优化问题得到状态反馈控制器增益及均方意义下吸引域的最大估计值.最后,数值算例验证了所得结论的有效性.

Stabilization for Piecewise Homogeneous Markov Jump Systems Subject to Actuator Saturation

The stabilization problem was studied for a class of Markov jump linear systems subject to actuator saturation， whose transition rates are piecewise homogeneous. Firstly， by using appropriate Lyapunov functional and ellipsoidal invariant set theory， the attraction domain of system in mean square sense was estimated to get the sufficient conditions with constraints of linear matrix inequalities for the closed-loop systems. Then， a convex optimization problem was solved to get the maximum domain of attraction in mean square sense and the state feedback controller gain. Finally， the effectiveness of the results was verified by a numerical example.