State Feedback Guaranteed Cost Controller for Nonlinear Time-Varying Delay Systems

This paper considers the problem of designing state feedback guaranteed cost controllers for a class of nonlinear systems with time-varying delay. The time delay is a continuous function belonging to a given interval and not required to be differentiable. By applying Lyapunov function method and linear matrix inequality (LMI) technique, new delay-dependent sufficient conditions for designing the state feedback guaranteed cost controller are derived. The method is also extended to handle system uncertainties in a straightforward way. A numerical example is given to illustrate the design procedure.

[1]  S. M. Lee,et al.  On robust stability for uncertain neural networks with interval time-varying delays , 2008 .

[2]  Zhi-Hong Guan,et al.  Delay-dependent output feedback guaranteed cost control for uncertain time-delay systems , 2004, Autom..

[3]  Ian R. Petersen,et al.  Optimal quadratic guaranteed cost control of a class of uncertain time-delay systems , 1997 .

[4]  T. K. C. Peng,et al.  Adaptive Guaranteed Cost of Control of Systems with Uncertain Parameters , 1970 .

[5]  Li Yu,et al.  An LMI approach to guaranteed cost control of linear uncertain time-delay systems , 1999, Autom..

[6]  Ju H. Park,et al.  Decentralized guaranteed cost dynamic control for synchronization of a complex dynamical network , 2012, 2012 12th International Conference on Control, Automation and Systems.

[7]  Emilia Fridman,et al.  On complete Lyapunov–Krasovskii functional techniques for uncertain systems with fast‐varying delays , 2008 .

[8]  Ju H. Park.  Delay-Dependent Criterion for Guaranteed Cost Control of Neutral Delay Systems , 2005 .

[9]  Li Yu,et al.  Exponential stability analysis for neutral switched systems with interval time-varying mixed delays and nonlinear perturbations , 2012 .

[10]  Arkadi Nemirovski,et al.  Lmi Control Toolbox For Use With Matlab , 2014 .

[11]  Wook Hyun Kwon,et al.  Delay-dependent guaranteed cost control for uncertain state-delayed systems , 2005, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[12]  Ju H. Park,et al.  Guaranteed cost synchronization of a complex dynamical network via dynamic feedback control , 2012, Appl. Math. Comput..

[13]  Oh-Min Kwon,et al.  Guaranteed cost control for uncertain large-scale systems with time-delays via delayed feedback , 2006 .

[14]  Jiuwen Cao.  Improved Delay-Dependent Stability Conditions for MIMO Networked Control Systems with Nonlinear Perturbations , 2014, TheScientificWorldJournal.

[15]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[16]  Jin Yang,et al.  Guaranteed Cost Controller Design of Networked Control Systems with State Delay , 2007 .

[17]  Nguyen Khoa Son,et al.  Stability radii of positive linear time-delay systems under fractional perturbations , 2009, Syst. Control. Lett..

[18]  Thongchai Botmart,et al.  Delay-dependent exponential stabilization for uncertain linear systems with interval non-differentiable time-varying delays , 2011, Appl. Math. Comput..

[19]  Shouming Zhong,et al.  Novel delay-dependent stability conditions for a class of MIMO networked control systems with nonlinear perturbation , 2008, Appl. Math. Comput..

[20]  Ian R. Petersen,et al.  LMI approach to suboptimal guaranteed cost control for uncertain time-delay systems , 1998 .

[21]  V. Kharitonov.  Time-Delay Systems: Lyapunov Functionals and Matrices , 2012 .

[22]  Vladimir L. Kharitonov,et al.  Time-Delay Systems , 2013 .

[23]  Vu Ngoc Phat,et al.  Optimal Guaranteed Cost Control of Linear Systems with Mixed Interval Time-Varying Delayed State and Control , 2012, J. Optim. Theory Appl..

[24]  Piyapong Niamsup,et al.  Stability analysis for a class of functional differential equations and applications , 2009 .

[25]  Xiushan Cai,et al.  Robust stability criteria for systems with interval time-varying delay and nonlinear perturbations , 2010, J. Comput. Appl. Math..

[26]  Ethelbert Nwakuche Chukwu,et al.  Stability and Time-Optimal Control of Hereditary Systems - With Application to the Economic Dynamics of the US - - - - 2nd Edition , 2002, Series on Advances in Mathematics for Applied Sciences.