\(H _{\infty }\) control and exponential stability of nonlinear nonautonomous systems with time-varying delay. (English) Zbl 1178.93047
Summary: This paper addresses the design of \(H _{\infty}\) 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 \(H _{\infty }\) 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.
MSC:
| 93B36 | \(H^\infty\)-control |
| 93C73 | Perturbations in control/observation systems |
| 93B52 | Feedback control |
| 93C10 | Nonlinear systems in control theory |
Keywords:
\(H _{\infty }\) control; exponential stability; nonlinear perturbation; time-varying delay; Riccati equationsReferences:
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