Observer-based output feedback stabilisation and ℒ2-disturbance attenuation of uncertain Hamiltonian systems with input and output delays

This paper is concerned with the problems of stabilisation and $\mathcal {L}_2 $L2-disturbance attenuation for a class of uncertain Hamiltonian systems in the presence of input and output time delays and external disturbances. The dissipativity structural property of the uncertain delayed Hamiltonian systems is fully exploited, and sufficient conditions are obtained by the use of Lyapunov–Krasovskii functional theorem and Luenberger-type observer to guarantee the asymptotical stability of the closed-loop systems for any given arbitrarily large yet bounded delays. An observer-based controller with an assistant reference input is designed corresponding to the external disturbances and time delay patterns. It is shown that the closed-loop systems under the feedback control law can guarantee the γ-dissipative inequalities be satisfied. The results are illustrated by the example of observer-based control of a power system.