Robust Adaptive Control and L2 Disturbance Attenuation for Uncertain Hamiltonian Systems with Time Delay

This paper deals with the robust stabilizability and L-2 disturbance attenuation for a class of time-delay Hamiltonian control systems with uncertainties and external disturbances. Firstly, the robust stability of the given systems is studied, and delay-dependent criteria are established based on the dissipative structural properties of the Hamiltonian systems and the Lyapunov-Krasovskii (L-K) functional approach. Secondly, the problem of L-2 disturbance attenuation is considered for the Hamiltonian systems subject to external disturbances. An adaptive control law is designed corresponding to the time-varying delay pattern involved in the systems. It is shown that the closed-loop systems under the feedback control law can guarantee the gamma-dissipative inequalities be satisfied. Finally, two numerical examples are provided to illustrate the theoretical developments.