Sliding mode H_∞ control for a class of uncertain nonlinear state-delayed systems  

作　　者：Wu Ligang Wang Changhong Gao Huijun Zhang Lixian 

机构地区：[1]Space Control and Inertial Technology Research Center, Harbin Inst. of Technology, Harbin 150001, P. R. China

出　　处：《Journal of Systems Engineering and Electronics》2006年第3期576-585,共10页系统工程与电子技术（英文版）

基　　金：This project was supported by the National Natural Science Foundation of China(69874008)

摘　　要：A new proportional-integral （PI） sliding surface is designed for a class of uncertain nonlinear state-delayed systems. Based on this, an adaptive sliding mode controller （ASMC） is synthesized, which guarantees the occurrence of sliding mode even when the system is undergoing parameter uncertainties and external disturbance. The resulting sliding mode has the same order as the original system, so that it becomes easy to solve the H∞ control problem by designing a memoryless H∞ state feedback controller. A delay-dependent sufficient condition is proposed in terms of linear matrix inequalities （LMIs）, which guarantees the sliding mode robust asymptotically stable and has a noise attenuation level γ in an H∞ sense. The admissible state feedback controller can be found by solving a sequential minimization problem subject to LMI constraints by applying the cone complementary linearization method. This design scheme combines the strong robustness of the sliding mode control with the H∞ norm performance. A numerical example is given to illustrate the effectiveness of the proposed scheme.A new proportional-integral （PI） sliding surface is designed for a class of uncertain nonlinear state-delayed systems. Based on this, an adaptive sliding mode controller （ASMC） is synthesized, which guarantees the occurrence of sliding mode even when the system is undergoing parameter uncertainties and external disturbance. The resulting sliding mode has the same order as the original system, so that it becomes easy to solve the H∞ control problem by designing a memoryless H∞ state feedback controller. A delay-dependent sufficient condition is proposed in terms of linear matrix inequalities （LMIs）, which guarantees the sliding mode robust asymptotically stable and has a noise attenuation level γ in an H∞ sense. The admissible state feedback controller can be found by solving a sequential minimization problem subject to LMI constraints by applying the cone complementary linearization method. This design scheme combines the strong robustness of the sliding mode control with the H∞ norm performance. A numerical example is given to illustrate the effectiveness of the proposed scheme.

关 键 词：sliding mode control H∞ control NONLINEARITY state-delayed system linear matrix inequality （LMIs） 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]