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

V. N. Phat () and Q. P. Ha ()
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V. N. Phat: Institute of Mathematics
Q. P. Ha: University of Technology Sydney

Journal of Optimization Theory and Applications, 2009, vol. 142, issue 3, No 10, 603-618

Abstract: 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 (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-009-9512-9

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