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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

Professor
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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