Robust stabilization and L2 disturbance attenuation of time-delay Hamiltonian control systems with uncertainties

In this paper, new results are established for the robust stabilizability and L₂ 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 a delay-dependent criterion is established based on the dissipative structural properties of the Hamiltonian systems and the Lyapunov-Krasovskii (L-K) functional approach. Secondly, the problem of L₂ disturbance attenuation is considered for the Hamiltonian systems subject to external disturbances. It is shown that the closed-loop systems under the adaptive feedback control law can guarantee the γ-dissipative inequalities be satisfied. Finally, several examples are provided to illustrate the theoretical developments.