一类切换系统的输出反馈H_∞控制

Output Feedback H_∞ Control for a Class of Impulsive Switched Systems

目的状态作为系统内部变量组,或由于不可能全部直接测量,或由于量测手段在经济性和适用性上的限制,从而使状态反馈物理实现成为不可能或很困难的事.状态反馈在性能上的不可替代性和在物理上的不能实现性,形成了一个尖锐的矛盾.解决这个矛盾通常需要采用动态输出反馈方案,也就是在反馈系统中单独或同时引入串联补偿器和并联补偿器,从而使输出反馈达到状态反馈功能.因此,针对一类具有扰动的脉冲切换系统,在任意切换的情况下研究了这类系统的渐近稳定问题和干扰抑制问题.方法利用线性矩阵不等式(LMI)、H∞控制理论和Lyapunov函数方法,同时采用变量替换法将条件转化为容易求解的线性矩阵不等式(LMI)形式.结果给出了这类具有扰动的脉冲切换系统渐近稳定且具有H∞性能的充分条件,最后通过一个仿真算例验证了文中结论的有效性.结论这种检验方法简化了计算过程,同时采用的Lyapunov函数方法也降低了保守性.

Objective The state is a system inner quantity set. It＇s impossibility to measure all these states directly, or the restriction of measurement means in the economy and the applicability, makes the physical realization of the state feedback impossible or very difficult. With state feedback in the performance of unsubstitutation and being unable to be achieved in the physics, a sharp contradiction arises. The dynamic output feedback controllers are designed to resolve the contradiction. Therefore, a class of impulsive switched systems with disturbance is considered. The robust stability problem and disturbance attenu ation problem are studied for this class of systems under arbitrary switching. Methods Using linear matrix inequality （LMI） , H∞, control theory and Lyapunov function, simultaneously, the condition is transformed into linear matrix inequality （LMI） form that is easy to solve with change of variable approach. Results Sufficient conditions for asymptotic stability and H∞ performance of the impulsive switched systems with disturbances are given. Finally, a numerical example is given to illustrate the efficiency of the result in this paper. Conclusion It is shown that the method not only simplifies the calculation process but also has less conservative.