H<inf>∞</inf> control and exponential stability of nonlinear nonautonomous systems with time-varying delay

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Journal Article
Journal of Optimization Theory and Applications, 2009, 142 (3), pp. 603 - 618
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This paper addresses the design of H∞ state feedback controllers for a class of nonlinear time-varying delay systems. The interesting features here are that the system in consideration is nonautonomous with fast-varying delays, the delay is also involved in the observation output, and the controllers to be designed satisfy some exponential stability constraints on the closed-loop poles. By using the proposed Lyapunov functional approach, neither a controllability assumption nor a bound restriction on nonlinear perturbations is required to obtain new sufficient conditions for the H∞ control. The conditions are derived in terms of a solution to the standard Riccati differential equations, which allows for simultaneous computation of the two bounds that characterize the stability rate of the solution. © Springer Science+Business Media, LLC 2009.
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