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H ∞ Control and Exponential Stability of Nonlinear Nonautonomous Systems with Time-Varying Delay

Author

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  • V. N. Phat

    (Institute of Mathematics)

  • Q. P. Ha

    (University of Technology Sydney)

Abstract

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.

Suggested Citation

  • V. N. Phat & Q. P. Ha, 2009. "H ∞ Control and Exponential Stability of Nonlinear Nonautonomous Systems with Time-Varying Delay," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 603-618, September.
    • Handle: RePEc:spr:joptap:v:142:y:2009:i:3:d:10.1007_s10957-009-9512-9
    DOI: 10.1007/s10957-009-9512-9
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    References listed on IDEAS

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    1. V. N. Phat & P. Niamsup, 2006. "Stabilization of Linear Nonautonomous Systems with Norm-Bounded Controls," Journal of Optimization Theory and Applications, Springer, vol. 131(1), pages 135-149, October.
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    Cited by:

    1. R. Sakthivel & R. Samidurai & S. M. Anthoni, 2010. "Asymptotic Stability of Stochastic Delayed Recurrent Neural Networks with Impulsive Effects," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 583-596, December.

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