一类不确定线性系统的混杂状态反馈H_∞鲁棒控制

在许多实际控制问题中,控制行为由若干个控制器之间相互切换所决定。利用混杂状态反馈控制策略研究一类不确定线性系统的H∞镇定问题。假定所考虑的系统存在有限个备选的静态状态反馈控制器,并且每个控制器的增益矩阵均已知。在每个单一的控制器均不能使系统稳定且具有H∞扰动衰减度的条件下,基于凸组合条件,通过切换律的设计,在这有限个控制器之间进行切换完成了对该系统H∞意义下的镇定。所得结果为线性系统H∞状态反馈控制的综合问题提供了更深的视角,混杂状态反馈控制有利于控制系统其它性能的实现。

Robust H∞ Control for a Class of Linear Systems With Norm-Bound Time-Varying Uncertainty via Hybrid State Feedback

There are many practical control problems where the control action is decided by switching among a given set of controllers. The hybrid state feedback H∞ stabilization problems for a class of linear systems with norm-bound time-varying uncertainty were studied. Finite static state feedback controllers were provided in a given set of controllers, and the gain matrix of state feedback controllers was known. Though none of the individual controllers can make the systems stable with H∞ disturbance attenuation, using convex combination condition, the switched linear system is shown to be stabilizable with an H∞ gain through the design switching laws. The results provide a deeper insight into the synthesis problems of the linear H∞ state feedback, hybrid state feedback H∞ control is helpful to perform other functions of control systems. Finally, a simulation example illustrates the main results in this paper.