L2增益约束下跳变系统鲁棒控制

不确定跳变系统的L2增益条件与系统可镇定性和鲁棒性密切相关,本文阐述利用依赖于模态的状态反馈鲁棒控制律,以实现闭环系统输入输出L2增益约束的要求,一方面用凸多面体界定跳变系统各模态间的跳变转移率的变化,另一方面,用L2增益界定对象状态方程中时变不确定参数,在一定概率空间下,获得的反馈控制律对不确定跳变概率和时变参数具有鲁棒性.反馈控制律的设计利用线性矩阵不等式技术,通过凸优化计算易于实现,最后给出了数值计算示例.

Robust control for jump systems with L-two gain constraints

The general quadratic L-two gain analysis of uncertain jump systems plays an important role to its stabilization and robustness.We present a robust control law with mode-dependent state feedback such that the resulting jump system satisfies given input-and-output L-two gain constraints.There are two components of uncertainty.First,the uncertainty of transition rate among different modes is bounded by a convex polytope.Second,the time-varying uncertain parameters of state equation are characterized by a selected L-two gain.Under a probability space,the obtained feedback control law is robust against the uncertainties of transition rate and time-varying parameters.Using linear matrix ioequality(LMI) technique and convex optimization computing,we can readily implement the synthesis of feedback control law.Finally,a computing example is given.