Brief paper: Exponential stability of linear distributed parameter systems with time-varying delays

Authors:
Emilia Fridman;Yury Orlov
Affiliations:
School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978, Israel;CICESE Research Center, Km.107, Carretera Tijuana-Ensenada, Ensenada, B.C. 22 860, Mexico
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

Exponential stability analysis via the Lyapunov-Krasovskii method is extended to linear time-delay systems in a Hilbert space. The operator acting on the delayed state is supposed to be bounded. The system delay is admitted to be unknown and time-varying with an a priori given upper bound on the delay. Sufficient delay-dependent conditions for exponential stability are derived in the form of Linear Operator Inequalities (LOIs), where the decision variables are operators in the Hilbert space. Being applied to a heat equation and to a wave equation, these conditions are reduced to standard Linear Matrix Inequalities (LMIs). The proposed method is expected to provide effective tools for stability analysis and control synthesis of distributed parameter systems.