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Journal of Optimization Theory and Applications

, Volume 142, Issue 3, pp 603–618 | Cite as

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

  • V. N. PhatEmail author
  • Q. P. Ha
Article

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.

Keywords

H control Exponential stability Nonlinear perturbation Time-varying delay Riccati equations 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Institute of MathematicsHanoiVietnam
  2. 2.Faculty of Engineering and Information TechnologyUniversity of Technology SydneySydneyAustralia

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