饱和非线性约束离散时间系统的H_∞控制Robust H_∞ Control of Discrete-Time Systems with Saturation Nonlinearities
冯青香;肖民卿;王留海;
摘要(Abstract)：
研究了一类带有饱和非线性状态约束的离散时间系统的H_∞控制问题.根据Lyapunov稳定性理论和线性矩阵不等式(LMI)处理方法,提出γ-次优H_∞状态反馈控制律存在的一个充分条件,通过求解相应的线性矩阵不等式给出了H_∞状态反馈控制器的设计方法.数值算例验证了文中所提方法的有效性.
关键词(KeyWords)： 线性离散时间系统;饱和非线性状态约束;H_∞控制;线性矩阵不等式
基金项目(Foundation): 福建省自然科学基金资助项目(2014J01222);; 福建省青年创新基金项目(2016J05003)
作者(Authors): 冯青香;肖民卿;王留海;
参考文献(References)：
- [1] GUILLARD H,MONACO S,NORMAND-CYOTR D. On H!-control of discrete-time nonlinear systems[J]. International Journal of Robust and Nonlinear Control,1996,6(7):663-643.
- [2] SHAIJU A J,PETERSEN I R. Discrete-time robust H!control of a class of nonlinear uncertain systems[J]. International Journal of Robust and Nonlinear Control,2013,23(14):1629-1641.
- [3] LIN W,BYMES C I. H!-control of discrete-time nonlinear systems[J]. IEEE Transactions on Automatic Control,1996,41(4):494-510.
- [4] SARAVANAKUMAR R,ALI M S,HUANG H,et al. Robust H!state-feedback control for nonlinear uncertain systems with mixed time-varying delays[J]. International Journal of Control,Automation and Systems,2018,16(1):225-233.
- [5] BEDIOUI N,SALHI S,KSOURI M. Robust stabilization approach and H!performance via static output feedback for a class of nonlinear systems[J]. Mathematical Problems in Engineering,2009,42(4):1-22.
- [6] GUO L,CHEN W H. Output feedback H!control for a class of uncertain nonlinear discrete-time delay systems[J]. Transactions of the Institute of Measurement and Control,2003,25(2):107-121.
- [7] ABBASZADEH M,MARQUES H J. LMI optimization approach to robust H!observer design and static output feedback stabilization for discrete-time nonlinear uncertain systems[J]. International Journal of Robust and Nonlinear Control,2009,19(3):313-340.
- [8] SINGH V. Stability analysis of discrete-time systems in a state-space realization with state saturation nonlinearities:linear matrix inequality approach[J]. IEE Proceedings Control Theory and Applications,2005,152(1):9-12.
- [9] KAR H. An LMI based criterion for the nonexistence of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic[J]. Digital Signal Processing,2007,17(2):685-689.
- [10] KANDANVLI V K R,KAR H. Robust stability of discrete-time state-delayed systems with saturation nonlinearities:linear matrix inequality approach[J]. Signal Processing,2009,89(2):161-173.
- [11] KANDANVLI V K R,KAR H. Delay-dependent stability criterion for discrete-time uncertain state-delayed systems employing saturation nonlinearities[J]. Arabian Journal for Science and Engineering,2013,38(10):2911-2920.
- [12]姚芳,肖民卿,唐超平,等.一类带有饱和非线性约束的离散时间系统保性能控制[J].福建师范大学学报(自然科学版),2015,31(1):26-31.
- [13] NABBEN R,VARGA R S. A linear algebra proof then inverse of a strictly diagonally dominant stieltjes matrix[J]. SIAM Journal of Matrix Analysis and Applications,1994,15(1):107-113.
- [14] MARTINEZ S,MICHON G,MARTIN J S. Inverse of strictly ultrametric matrices are of stieltjes type[J]. SIAM Journal of Matrix Analysis and Applications,1994,15(1):98-106.
- [15]俞立.鲁棒控制-线性矩阵不等式处理方法[M].北京:清华大学出版社,2002.