Delay-dependent decentralised control for a class of uncertain similar interconnected systems with state delay and input delay

In this paper, the problem of delay-dependent decentralised control for a class of uncertain similar interconnected systems is investigated, where not only the state vectors but also the input vectors involve time delay. The new similar structure is presented via state feedback, based on which, by exploiting the structure of interconnected systems, the new integral inequalities, constrained Lyapunov equations and LMI method, the decentralised stabilization controllers are designed, which is dependent on time delays, to stabilise the interconnected systems uniformly asymptotically. The results show that the design is easy to calculate and the controllers have the similar structure, so it is easy to realise project. Finally, a numerical example is given to demonstrate the effectiveness of the results obtained in this paper.

[1]  Kazuo Murota,et al.  Symmetric failures in symmetric control systems , 2000 .

[2]  Jiang Chang-sheng.  Robust Decentralized Stabilization For Uncertain Time-delay Interconnected Systems with Input Delay , 2009 .

[3]  Stephen P. Banks,et al.  Lie algebras and the stability of nonlinear systems , 1994 .

[4]  Lihua Xie,et al.  Robust H/sub infinity / control for linear systems with norm-bounded time-varying uncertainty , 1992 .

[5]  Shi Hai.  Robust control for generalized interconnected systems with similar structures , 2003 .

[6]  Zidong Wang,et al.  Quantized $H_{\infty }$ Control for Nonlinear Stochastic Time-Delay Systems With Missing Measurements , 2012, IEEE Transactions on Automatic Control.

[7]  L. Xie,et al.  Robust H^∞ Control for Linear Systems with Norm-Bounded Time-Varying Uncertainty , 1990 .

[8]  P. Shi,et al.  Decentralized robust model reference adaptive control for interconnected time-delay systems , 2004, Proceedings of the 2004 American Control Conference.

[9]  Zhang Si-ying.  The Similar Structures and Control Problems of Complex Systems , 2002 .

[10]  Zidong Wang,et al.  Finite-horizon H∞ fault estimation for linear discrete time-varying systems with delayed measurements , 2013, Autom..

[11]  Guo-Ping Liu,et al.  Output Feedback Stabilization for a Discrete-Time System With a Time-Varying Delay , 2008, IEEE Transactions on Automatic Control.

[12]  Lubomír Bakule,et al.  Decentralized control: An overview , 2008, Annu. Rev. Control..

[13]  E. Davison.  Brief paper: The decentralized stabilization and control of a class of unknown non-linear time-varying systems , 1974 .

[14]  ZHANGSi－ying.  The Similar Structures and Control Problems of Complex Systems , 2002 .

[15]  Vu Ngoc Phat,et al.  Decentralized H∞ control for large-scale interconnected nonlinear time-delay systems via LMI approach , 2012 .

[16]  Liu Xiaoping,et al.  Output regulation of strongly coupled symmetric composite systems , 1992 .

[17]  Zhong-Ping Jiang,et al.  Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems , 2007, Autom..

[18]  Xiaoping Liu.  Output regulation of strongly coupled symmetric composite systems , 1992, Autom..

[19]  Xing-Gang Yan,et al.  Design of Robust Controllers with Similar Structure for Nonlinear Uncertain Composite Large-Scale Sy , 1997 .

[20]  Bing Chen,et al.  New results on delay-dependent robust stability of uncertain time delay systems , 2010, Int. J. Syst. Sci..

[21]  Huijun Gao,et al.  A New Model Transformation of Discrete-Time Systems With Time-Varying Delay and Its Application to Stability Analysis , 2011, IEEE Transactions on Automatic Control.

[22]  Guang-Hong Yang,et al.  Decentralized robust control for interconnected systems with time-varying uncertainties , 1996, Autom..

[23]  P. Balasubramaniam,et al.  Delay-dependent robust H ∞ control for uncertain stochastic T–S fuzzy systems with time-varying state and input delays , 2011, Int. J. Syst. Sci..

[24]  J. Rodellar,et al.  Decentralised control design of uncertain nominally linear symmetric composite systems , 1996 .

[25]  Huijun Gao,et al.  ${H}_{\infty }$ Filtering for Discrete-Time State-Delayed Systems With Finite Frequency Specifications , 2011, IEEE Transactions on Automatic Control.

[26]  Zhang Qing-ling,et al.  Decentralized control for nonlinear lager-scale interconnected systems with input saturation , 2007 .

[27]  Guang-Hong Yang,et al.  Decentralized control of a class of large-scale systems with symmetrically interconnected subsystems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[28]  Wen-June Wang,et al.  Stabilization and estimation for perturbed discrete time-delay large-scale systems , 1997, IEEE Trans. Autom. Control..

[29]  Guang-Hong Yang,et al.  Structural properties of large-scale systems possessing similar structures , 1995, Autom..

[30]  Qing-Long Han,et al.  Delay-dependent H ∞ control of linear discrete-time systems with an interval-like time-varying delay , 2008, Int. J. Syst. Sci..

[31]  Lihua Xie,et al.  Reduced-order control for a class of nonlinear similar interconnected systems with mismatched uncertainty , 2003, Autom..

[32]  Xing-Gang Yan,et al.  Decentralized Output Feedback Robust Control for Nonlinear Large-scale Systems , 1998, Autom..

[33]  Masao Ikeda,et al.  Decentralized stabilization of linear time-varying systems , 1980 .

[34]  Changchun Hua,et al.  Decentralized MRAC for large-scale interconnected systems with time-varying delays and applications to chemical reactor systems , 2012 .