非线性奇异时滞系统的鲁棒同时保性能优化控制  

Robust Simultaneous Guaranteed Cost Control for Nonlinear Singular Systems with Time-Delay

作　　者：李瑞杰[1] 包俊东[1] 

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《兵器装备工程学报》2016年第4期149-154,共6页Journal of Ordnance Equipment Engineering

基　　金：内蒙古师范大学2014年度研究生科研创新基金(CXJJS14054)

摘　　要：针对一组非线性奇异时滞系统的鲁棒同时保性能控制问题进行研究,用范数有界的不确定参数的微分方程组描述所考虑的系统;基于Lyapunov-Krasovskii泛函和线性矩阵不等式方法给出存在同时保性能控制器的充分条件;对具有线性矩阵不等式约束的凸优化问题求解,进而明确给出使得性能指标函数上界达到最优值控制器的表达式;该控制器的设计方法不仅使得奇异时滞闭环系统组正则、无脉冲、同时鲁棒稳定,而且性能函数上界最优;最后,给出算例验证该方法的有效性。The simultaneous guaranteed cost control problem for a group of nonlinear singular systems with time-delay robust was studied. The systems under consideration were described by differential equations which were with norm-bounded and uncertain parameters. A sufficient condition for the existence of simultaneous guaranteed cost controller was derived by the approach which based on Lyapunov-Krasovskii functional and linear matrix inequality （LMI）. A convex optimization problem with LMI constraints was formulated, and controller which minimizes upper bound of cost index function was designed exactly. This design method makes sure that closed-loop of singular systems with time delay is not only regular, impulse free, robust stable but also upper bound of cost index function up to minimum. Finally, a numerical example was provided to demonstrate the availability of the proposed method.

关 键 词：非线性奇异系统 时滞 不确定 同时保性能控制 线性矩阵不等式 

分 类 号：O231.2[理学—运筹学与控制论]