H ∞ Control and Exponential Stability of Nonlinear Nonautonomous Systems with Time-Varying Delay
- 148 Downloads
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.
KeywordsH∞ control Exponential stability Nonlinear perturbation Time-varying delay Riccati equations
Unable to display preview. Download preview PDF.
- 3.Udwadia, F.E., Hosseini, M., Chen, Y.: Robust control of uncertain systems with time varying delays in control input. In: Proceedings of the American Control Conference, USA, pp. 3840–3845 (1997) Google Scholar
- 16.Boyd, S., Il Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in Systems and Control Theory. Studies in Applied Mathematics. SIAM, Philadelphia (1994) Google Scholar
- 20.Parlakci, M.N.A.: Improved robust stability criteria for time delay systems with nonlinear perturbations. In: Proc. of ICCA Conference, Budapest, June 2005, pp. 341–346 Google Scholar
- 22.William Thomas, R.: Riccati Differential Equations. Academic Press, San Diego (1972) Google Scholar