∞8 filter design for a class of nonlinear time-delay Hamiltonian systems

This paper investigates the ∞₈ filter design problem for a class of nonlinear time-delay Hamiltonian systems. Both state equations and output equations of the systems contain uncertain time delays. The process and measurement noises of the systems studied have unknown statistical characteristics and bounded energies. Based on the Lyapunov-Krasovskii stability theorem and the structural characteristics of Hamiltonian systems, a Hamiltonian dynamic filter architecture is proposed, and a new filter design method is developed. The nonlinear ∞₈ filter designed by the method can guarantee the ∞₈ performances. The parameters of the designed filter can be obtained by solving a special kind of inequalities. An illustrative example shows that the ∞₈ filter design method proposed in this paper is very effective.