Abstract
AbstractThis paper establishes new robust delay‐dependent stability and stabilization methods for a class of nominally linear continuous‐time systems with time‐varying delays. The parameter uncertainties are convex‐bounded and the unknown nonlinearities are time‐varying perturbations satisfying Lipschitz conditions in the state and delayed state. An appropriate Lyapunov functional is constructed to exhibit the delay‐dependent dynamics via descriptor format. Delay‐dependent stability analysis is performed to characterize linear matrix inequalities (LMIs)‐based conditions under which the nominally linear delay system is robustly asymptotically stable with a γ‐level ℒ︁2‐gain. Then we design delay‐dependent feedback stabilization schemes: a static one based on state‐measurements and a dynamic one based on observer‐based output feedback. In both schemes, the closed‐loop feedback system enjoys the delay‐dependent asymptotic stability with a prescribed γ‐level ℒ︁2‐gain. The feedback gains are determined by convex optimization over LMIs. All the developed results are tested on a representative example. Copyright © 2009 John Wiley & Sons, Ltd.
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