Several Types Of The Uncertain Time-delay Hamilton System Stability And The Analysis Of L2 Disturbance Rejection

As an important class of nonlinear systems, port-controlled Hamiltonian systems haveattracted increasing attentions in the feld of nonlinear control theory. But there is seldomresearching for uncertain Hamiltonian systems with time-delay. Systems with unknowndelayed states are often encountered in practice. The delay and the uncertainties are theprimary cause for leading unstable. Because of the complexity of the nonlinear systems,it is difcult in designing control. However, due to its nice structure with clear physicalmeaning, the PCH system has drawn a good deal of attention in practical control designs.So Hamiltonion systems have drawn increasing attention in the feld of nonlinear controlsystems.This paper is divided into the following two parts:1. Robust adaptive control and L₂disturbance attenuation for uncertain Hamiltoniansystems with time-Delay. This part deals with the robust stabilizability and L₂distur-bance attenuation for a class of time-delay Hamiltonian control systems with uncertaintiesand external disturbances. Firstly, the robust stability of the given systems is studied andboth delay-independent and delay-dependent criteria are established based on the dissipa-tive structural properties of the Hamiltonian systems and the Lyapunov-Krasovskii （L-K）functional approach. Secondly, the problem of L₂disturbance attenuation is considered forthe Hamiltonian systems subject to external disturbances. Two kinds of adaptive controllaws are designed corresponding to two cases of time-delay patterns involved in the systems.It is shown that the closed-loop systems under the feedback control laws can guarantee theγ-dissipative inequalities be satisfed. Finally, several numerical examples are provided toillustrate the theoretical developments.2. L₂Disturbance attenuation for a class of neutral Hamiltonian systems with time-delayand uncertainties. This paper deals with the L₂disturbance attenuation problem for a classof neutral time-varying delay Hamiltonian control systems with parametric uncertaintiesand external disturbances. Firstly, a delay-dependent stability criterion is proposed basedon Lyapunov-Krasovskii （L-K） functional approach for the neutral Hamiltonian systemswithout uncertainties and disturbances. Secondly, the problem of L₂disturbance attenuationis considered and an adaptive feedback control law, as well as a γ-dissipative inequality areconstructed. With these, a sufcient condition of asymptotically stability for the resultedclosed-loop systems is presented. Finally, two numerical examples are provided to illustrate the theoretical developments.Usually, we can design the adaptive controller to deal with the stabilization of nonlinearsystems with uncertainties. It makes the close-loop systems under the feed-back controllaw asymptotically stable. But, it is difcult to design the control law of the nonlinearsystems. Especially the systems are the time-delay nonlinear systems. This paper simplifedthe research process by using the especially structure of Hamilton system.