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

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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.

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Authors and Affiliations

  1. Institute of Mathematics, Hanoi, Vietnam

    V. N. Phat

  2. Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, Australia

    Q. P. Ha

Authors
  1. V. N. Phat
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  2. Q. P. Ha
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Corresponding author

Correspondence to V. N. Phat.

Additional information

Communicated by F.E. Udwadia.

This work was supported by the National Foundation for Science and Technology Development, Vietnam and the Center of Excellence for Autonnomous Systems funded by the Australian Research Council, Australia.

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Phat, V.N., Ha, Q.P. H ∞ Control and Exponential Stability of Nonlinear Nonautonomous Systems with Time-Varying Delay. J Optim Theory Appl 142, 603–618 (2009). https://doi.org/10.1007/s10957-009-9512-9

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  • DOI: https://doi.org/10.1007/s10957-009-9512-9

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