Delay-Dependent Guaranteed Cost Controller Design for Uncertain Neural Networks with Interval Time-Varying Delay

This paper studies the problem of guaranteed cost control for a class of uncertain delayed neural networks. The time delay is a continuous function belonging to a given interval but not necessary to be differentiable. A cost function is considered as a nonlinear performance measure for the closed-loop system. The stabilizing controllers to be designed must satisfy some exponential stability constraints on the closed-loop poles. By constructing a set of augmented Lyapunov-Krasovskii functionals combined with Newton-Leibniz formula, a guaranteed cost controller is designed via memoryless state feedback control, and new sufficient conditions for the existence of the guaranteed cost state feedback for the system are given in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the obtained result.

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

[2]  Ping Xiong,et al.  Guaranteed cost synchronous control of time-varying delay cellular neural networks , 2011, Neural Computing and Applications.

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

[4]  Li Yu,et al.  Optimal guaranteed cost control of discrete-time uncertain systems with both state and input delays , 2001, J. Frankl. Inst..

[5]  Ju H. Park.  On global stability criterion for neural networks with discrete and distributed delays , 2006 .

[6]  Shengyuan Xu,et al.  A survey of linear matrix inequality techniques in stability analysis of delay systems , 2008, Int. J. Syst. Sci..

[7]  Ju H. Park,et al.  On guaranteed cost control of neutral systems by retarded integral state feedback , 2005, Appl. Math. Comput..

[8]  Ju H. Park,et al.  Guaranteed cost control of uncertain nonlinear neutral systems via memory state feedback , 2005 .

[9]  Min Wu,et al.  LMI-based stability criteria for neural networks with multiple time-varying delays , 2005 .

[10]  M. N. Alpaslan Parlakçi,et al.  Robust delay-dependent guaranteed cost controller design for uncertain neutral systems , 2009, Appl. Math. Comput..

[11]  Patrick van der Smagt,et al.  Introduction to neural networks , 1995, The Lancet.

[12]  Ju H. Park.  A novel criterion for global asymptotic stability of BAM neural networks with time delays , 2006 .

[13]  Daming Shi,et al.  Introduction to Neural Networks , 2009 .

[14]  Hanlin He,et al.  Algebraic condition of synchronization for multiple time-delayed chaotic Hopfield neural networks , 2010, Neural Computing and Applications.

[15]  Kreangkri Ratchagit,et al.  Asymptotic Stability of Delay-Difference System of Hopfield Neural Networks via Matrix Inequalities and Application , 2007, Int. J. Neural Syst..

[16]  Emilia Fridman,et al.  Exponential stability of linear distributed parameter systems with time-varying delays , 2009, Autom..

[17]  S. Arik.  An improved global stability result for delayed cellular neural networks , 2002 .

[18]  Lu Yan,et al.  Guaranteed Cost Stabilization of Time-varying Delay Cellular Neural Networks via Riccati Inequality Approach , 2011, Neural Processing Letters.

[19]  Ju H. Park,et al.  Exponential stability analysis for uncertain neural networks with interval time-varying delays , 2009, Appl. Math. Comput..

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

[21]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[22]  Yong He,et al.  Stability Analysis and Robust Control of Time-Delay Systems , 2010 .

[23]  Hieu Minh Trinh,et al.  Exponential Stabilization of Neural Networks With Various Activation Functions and Mixed Time-Varying Delays , 2010, IEEE Transactions on Neural Networks.

[24]  Ju H. Park,et al.  Guaranteed cost control of time-delay chaotic systems , 2006 .

[25]  Ping Xiong,et al.  Lr-synchronization and adaptive synchronization of a class of chaotic Lurie systems under perturbations , 2011, J. Frankl. Inst..

[26]  Ju H. Park.  Dynamic output guaranteed cost controller for neutral systems with input delay , 2005 .

[27]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Hanlin He,et al.  Guaranteed Cost Synchronization of Chaotic Cellular Neural Networks with Time-Varying Delay , 2012, Neural Computation.

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