Technical Brief

Robust Nonfragile Stabilizing Controller for an Uncertain Stochastic Nonlinear System With Interval Time-Varying State-Delays: Prescribed H Performance Level

[+] Author and Article Information
K. Ramakrishnan

Assistant Professor
Department of Electrical and Electronics Engineering,
Pondicherry Engineering College,
Pondicherry 605014, India
e-mail: ramkieeiit@gmail.com

G. Ray

Department of Electrical Engineering,
Indian Institute of Technology Kharagpur,
West Bengal 721302, India
e-mail: gray@ee.iitkgp.ernet.in

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 28, 2013; final manuscript received May 2, 2014; published online July 10, 2014. Assoc. Editor: John B. Ferris.

J. Dyn. Sys., Meas., Control 136(5), 054505 (Jul 10, 2014) (3 pages) Paper No: DS-13-1254; doi: 10.1115/1.4027727 History: Received June 28, 2013; Revised May 02, 2014

In this technical brief, delay-dependent nonfragile H control problem of a class of stochastic nonlinear systems with interval time-varying state-delays has been considered using Lyapunov–Krasovskii (LK) functional approach. By exploiting a candidate LK functional and using free-weighting matrix technique, a less conservative delay-dependent stabilization criterion is presented for the existence of a nonfragile memoryless state-feedback controller, which ensures stochastic stability as well as a prescribed H performance level of the closed-loop system in the presence admissible parametric uncertainties in the system as well as in the controller gains and exogenous input signal. Since the resulting stabilization criterion is in terms of nonlinear matrix inequalities (NLMIs), it is solved using cone complementarity algorithm (CCA) to obtain a stabilizing controller. A numerical example is presented to illustrate the effectiveness of the proposed result.

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Xu, S., Lam, J., Wang, J., and Yang, G., 2004, “Non-Fragile Positive Real Control for Uncertain Linear Neutral Delay Systems,” Syst. Control Lett., 52(1), pp. 59–74. [CrossRef]
Li, L., and Jia, Y., 2009, “Non-Fragile Dynamic Output Feedback Control for Linear Systems With Time-Varying Delay,” IET Control Theory Appl., 3(8), pp. 995–1005. [CrossRef]
Li, H., and Shi, Y., 2012, “Robust H Filtering for Nonlinear Stochastic Systems With Uncertainties and Random Delays Modeled by Markov Chains,” Automatica, 48(1), pp. 159–166. [CrossRef]
Li, H., and Shi, Y., 2012, “State-Feedback H Control for Stochastic Time-Delay Nonlinear Systems With State and Disturbance-Dependent Noise,” Int. J. Control, 85(10), pp. 1515–1531. [CrossRef]
Keel, L., and Bhattacharyya, S., 1997, “Robust, Fragile or Optimal,” IEEE Trans. Autom. Control, 42(8), pp. 1098–1105. [CrossRef]
Friedman, E., and Shaked, U., 2003, “Delay-Dependent Stability and H Control: Constant and Time-Varying Delays,” Int. J. Control, 76(1), pp. 48–60. [CrossRef]
Wang, D. J., 2004, “A New Approach to Delay-Dependent H Control of Linear State-Delayed Systems,” ASME J. Dyn. Syst. Meas. Control, 126(1), pp. 201–205. [CrossRef]
Xu, S., Lam, J., Yang, G. H., and Wang, J., 2006, “Stabilization and H Control for Uncertain Stochastic Time-Delay Systems via Non-Fragile Controllers,” Asian J. Control, 8(2), pp. 197–200. [CrossRef]
Zhang, J., Shi, P., and Yang, H., 2009, “Non-Fragile Robust Stabilization and H Control for Uncertain Stochastic Nonlinear Time-Delay Systems,” Chaos Solitons Fractals, 42(5), pp. 3187–3196. [CrossRef]
Wang, D., Shi, P., Wang, W., and Karimi, H. R., “Non-Fragile H Control for Switched Stochastic Delay Systems With Application to Water Quality Process,” Int. J. Robust Nonlinear Control (to be published) [CrossRef].
Wang, C., and Shen, Y., 2011, “Delay-Dependent Non-Fragile Robust Stabilization and H Control of Uncertain Stochastic Systems With Time-Varying Delay and Nonlinearity,” J. Franklin Inst., 348(8), pp. 2174–2190. [CrossRef]
Yue, D., Tian, E., and Zhang, Y., 2009, “A Piecewise Analysis Method to Stability Analysis of Linear Continuous/Discrete Systems With Time-Varying Delay,” Int. J. Robust Nonlinear Control, 19(13), pp. 1493–1518. [CrossRef]
Ramakrishnan, K., 2014, “Robust Stability and Stabilization on Interval State-Delayed Systems,” Ph.D. thesis, Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, West Bengal, India.




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