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Research Papers

Robust Absolute Stability Criteria for Uncertain Lurie System With Interval Time-Varying Delay

[+] Author and Article Information
Pankaj Mukhija

Department of Electrical and
Electronics Engineering,
National Institute of Technology Delhi,
Delhi 110040, India
e-mail: pankaj.mukhija@gmail.com

Indra Narayan Kar

Department of Electrical Engineering,
Indian Institute of Technology Delhi,
New Delhi 110016, India
e-mail: ink@ee.iitd.ac.in

Rajendra K. P. Bhatt

Professor
Department of Electrical Engineering,
Indian Institute of Technology Delhi,
New Delhi 110016, India
e-mail: rkpb@ee.iitd.ac.in

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 3, 2012; final manuscript received February 9, 2014; published online April 28, 2014. Assoc. Editor: Sean Brennan.

J. Dyn. Sys., Meas., Control 136(4), 041020 (Apr 28, 2014) (7 pages) Paper No: DS-12-1247; doi: 10.1115/1.4026872 History: Received August 03, 2012; Revised February 09, 2014

This paper addresses the problem of absolute stability of Lurie system with interval time-varying delay. The delay range is divided into two equal segments and an appropriate Lyapunov–Krasovskii functional (LKF) is defined. A tighter bounding technique for the derivative of LKF is developed. This bounding technique in combination with the Wirtinger inequality is used to develop the absolute stability criterion in terms of linear matrix inequalities (LMIs). The stability analysis is also extended to the Lurie system with norm-bounded parametric uncertainties. The effectiveness of the proposed approach has been illustrated through a numerical example and Chua's oscillator.

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