Reliable control for linear systems with time-varying delays and parameter uncertainties

ABSTRACT In this paper, reliable control for linear systems with time-varying delays and parameter uncertainties is considered. By constructing newly augmented Lyapunov–Krasovskii functionals and utilizing some mathematical techniques such as Leibnitz's rule, Schur's complement, reciprocally convex combination, and so on, a reliable controller design method for linear systems with time-varying delays and parameter uncertainties will be suggested in Theorem 1. Based on the result of Theorem 1, a non-reliable stabilization criterion will be presented in Corollary 1. Theorem 1 and Corollary 1 are derived within the framework of linear matrix inequalities(LMIs) which can be easily solved by utilizing various optimization algorithms. Two numerical examples are included to show the effectiveness and necessity of the proposed results.

[1]  Robert E. Skelton,et al.  Stability tests for constrained linear systems , 2001 .

[2]  Engang Tian,et al.  Brief Paper Robust fault-tolerant control of networked control systems with stochastic actuator failure , 2010 .

[3]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[4]  El-Kebir Boukas,et al.  Deterministic and Stochastic Time-Delay Systems , 2002 .

[5]  Emilia Fridman,et al.  An improved stabilization method for linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[6]  YUQIONG LIU,et al.  Reliable Control of Uncertain Nonlinear Systems , 1998, Autom..

[7]  Myeong-Jin Park,et al.  Reliable Control for Linear Dynamic Systems with Time-varying Delays and Randomly Occurring Disturbances , 2014 .

[8]  Yisha Liu,et al.  Robust reliable control for discrete‐time‐delay systems with stochastic nonlinearities and multiplicative noises , 2011 .

[9]  W. Marsden.  I and J , 2012 .

[10]  Zhou Luan-jie,et al.  Delay-Dependent Robust Stabilization of Uncertain State-Delayed Systems , 2004 .

[11]  E. Fridman,et al.  Delay-dependent stability and H ∞ control: Constant and time-varying delays , 2003 .

[12]  Young Soo Moon,et al.  Delay-dependent robust stabilization of uncertain state-delayed systems , 2001 .

[13]  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).

[14]  Lei Guo,et al.  Delay‐range‐dependent robust stability and stabilization for uncertain systems with time‐varying delay , 2008 .

[15]  Ju H. Park,et al.  Robust fault-tolerant H∞ control for offshore steel jacket platforms via sampled-data approach , 2015, J. Frankl. Inst..

[16]  Ting Wang,et al.  Further stability criteria on discrete-time delayed neural networks with distributeddelay , 2013, Neurocomputing.

[17]  Frédéric Gouaisbaut,et al.  Wirtinger-based integral inequality: Application to time-delay systems , 2013, Autom..

[18]  Shenquan Wang,et al.  Reliable Fuzzy Control for a Class of Nonlinear Networked Control Systems with Time Delay , 2012 .

[19]  Rathinasamy Sakthivel,et al.  Robust reliable H∞ control for stochastic neural networks with randomly occurring delays , 2015, Neurocomputing.

[20]  Goshaidas Ray,et al.  State feedback stabilization of uncertain linear time-delay systems: A nonlinear matrix inequality approach , 2011, Numer. Linear Algebra Appl..

[21]  Xinzhi Liu,et al.  On design of robust reliable H∞ control and input-to-state stabilization of uncertain stochastic systems with state delay , 2013, Commun. Nonlinear Sci. Numer. Simul..

[22]  Long-Yeu Chung,et al.  Robust reliable Hinfinity control for uncertain nonlinear systems via LMI approach , 2008, Appl. Math. Comput..

[23]  S. M. Lee,et al.  New augmented Lyapunov–Krasovskii functional approach to stability analysis of neural networks with time-varying delays , 2014 .

[24]  Ju H. Park,et al.  Improved results on stability of linear systems with time-varying delays via Wirtinger-based integral inequality , 2014, J. Frankl. Inst..

[25]  Guoping Liu,et al.  Delay‐dependent stability and stabilization of neutral time‐delay systems , 2009 .

[26]  Rathinasamy Sakthivel,et al.  Robust Reliable Control for Neutral-Type Nonlinear Systems with Time-Varying Delays , 2014 .