NEW H1 CONTROL DESIGN FOR POLYTOPIC SYSTEMS WITH MIXED TIME-VARYING DELAYS IN STATE AND INPUT

This paper concerns with the problem of state-feedback H1 control design for a class of linear systems with polytopic uncertainties and mixed time-varying delays in state and input. Our approach can be described as follows. We first construct a state-feedback controller based on the idea of parameter-dependent controller design. By constructing a new parameter-dependent Lyapunov-Krasovskii functional (LKF), we then derive new delay-dependent conditions in terms of linear matrix inequalities ensuring the exponential stability of the corresponding closed-loop system with a H1 disturbance atten- uation level. The effectiveness and applicability of the obtained results are demonstrated by practical examples. Keywords: Polytopic uncertainties, H1 control, Time-varying delays, Input delayed, Linear matrix inequalities

[1]  Zhi-Gang Wu,et al.  Stabilization of switched delay systems with polytopic uncertainties under asynchronous switching , 2013, J. Frankl. Inst..

[2]  Keqin Gu,et al.  Stability and Stabilization of Systems with Time Delay , 2011, IEEE Control Systems.

[3]  P. Khargonekar,et al.  H ∞ control of linear time-varying systems: a state-space approach , 1991 .

[4]  Vu Ngoc Phat,et al.  Exponential stability and stabilization of a class of uncertain linear time-delay systems , 2009, J. Frankl. Inst..

[5]  Hamid Reza Karimi,et al.  Robust Control of Stochastic Systems Against Bounded Disturbances With Application to Flight Control , 2014, IEEE Transactions on Industrial Electronics.

[6]  Andrey Polyakov,et al.  Output stabilization of time-varying input delay systems using interval observation technique , 2013, Autom..

[7]  Quang Phuc Ha,et al.  Stability and stabilization of switched linear dynamic systems with time delay and uncertainties , 2009, Appl. Math. Comput..

[8]  Armand Toguyéni,et al.  A Switched System Approach to Exponential Stabilization Through Communication Network , 2012, IEEE Transactions on Control Systems Technology.

[9]  Silviu-Iulian Niculescu,et al.  Survey on Recent Results in the Stability and Control of Time-Delay Systems* , 2003 .

[10]  Vu Ngoc Phat,et al.  New exponential estimate for robust stability of nonlinear neutral time-delay systems with convex polytopic uncertainties , 2011 .

[11]  Hamid Reza Karimi,et al.  A robust fault detection design for uncertain Takagi–Sugeno models with unknown inputs and time-varying delays , 2014 .

[12]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..

[13]  Hamid Reza Karimi,et al.  Output-Feedback-Based $H_{\infty}$ Control for Vehicle Suspension Systems With Control Delay , 2014, IEEE Transactions on Industrial Electronics.

[14]  Hieu Minh Trinh,et al.  A new approach to state bounding for linear time-varying systems with delay and bounded disturbances , 2014, Autom..

[15]  Ligang Wu,et al.  Induced l2 filtering of fuzzy stochastic systems with time-varying delays , 2013, IEEE Transactions on Cybernetics.

[16]  Vu Ngoc Phat,et al.  New H∞ Controller Design for Neural Networks with Interval Time-Varying Delays in State and Observation , 2012, Neural Processing Letters.

[17]  Hamid Reza Karimi,et al.  Stability analysis and H∞ controller synthesis of discrete-time switched systems with time delay , 2014, Syst. Control. Lett..

[18]  P. Shi,et al.  Exponential H∞ filtering for switched linear systems with interval time‐varying delay , 2009 .

[19]  Hamid Reza Karimi,et al.  Network-based H∞ output feedback control for uncertain stochastic systems , 2013, Inf. Sci..

[20]  Vu Ngoc Phat,et al.  Delay feedback control in exponential stabilization of linear time-varying systems with input delay , 2009, IMA J. Math. Control. Inf..

[21]  Yuanqing Xia,et al.  Parameter-dependent robust H∞ filtering for uncertain discrete-time systems , 2009, Autom..

[22]  E. Boukas,et al.  H∞ control of switched linear discrete‐time systems with polytopic uncertainties , 2006 .

[23]  Huijun Gao,et al.  Parameter-dependent robust stability of uncertain time-delay systems , 2007 .

[24]  P. T. Nam,et al.  Robust exponential stability and stabilization of linear uncertain polytopic time-delay systems , 2008 .

[25]  Mohamed Yagoubi,et al.  On State Feedback H∞ Control for Discrete-Time Singular Systems , 2013, IEEE Transactions on Automatic Control.

[26]  Hieu Minh Trinh,et al.  Design of H∞ control of neural networks with time-varying delays , 2012, Neural Computing and Applications.

[27]  Fei Liu,et al.  H∞ Filtering for Discrete-Time Systems With Stochastic Incomplete Measurement and Mixed Delays , 2012, IEEE Trans. Ind. Electron..

[28]  Q. P. Ha,et al.  Parameter-dependent H∞ Control for Time-varying Delay Polytopic Systems , 2010, J. Optim. Theory Appl..

[29]  Peng Shi,et al.  Robust quantized H∞ control for network control systems with Markovian jumps and time delays , 2013 .

[30]  Yongduan Song,et al.  A Novel Control Design on Discrete-Time Takagi–Sugeno Fuzzy Systems With Time-Varying Delays , 2013, IEEE Transactions on Fuzzy Systems.

[31]  Ai-Guo Wu,et al.  Robust H-infinity estimation for linear time-delay systems: An improved LMI approach , 2009 .

[32]  V. Phat,et al.  H∞ control for nonlinear time-varying delay systems with convex polytopic uncertainties , 2010 .

[33]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

[34]  Hamid Reza Karimi,et al.  Observer-based finite-time fuzzy H∞ control for discrete-time systems with stochastic jumps and time-delays , 2014, Signal Process..

[35]  Vu Ngoc Phat,et al.  Robust stabilization of linear polytopic control systems with mixed delays , 2010 .

[36]  Hieu Trinh,et al.  New results on state bounding for discrete-time systems with interval time-varying delay and bounded disturbance inputs , 2014 .

[37]  Tyrone Fernando,et al.  Output feedback guaranteed cost control of uncertain linear discrete systems with interval time-varying delays , 2013 .

[38]  Hamid Reza Karimi,et al.  Robust Control of Continuous-Time Systems With State-Dependent Uncertainties and Its Application to Electronic Circuits , 2014, IEEE Transactions on Industrial Electronics.