Robust Stabilization Of An Input Delay Hamiltonian System With Saturation Constraints

In practical applications,many controlled systems such as communication systems,electric networks and engineering systems usually appear some phenomenon that includes saturation,time-delay and uncertainty.In recent decades,it has produced a large number of stable and controlled research results for time-delayed systems under the saturation and restriction.However,most of results are all about the linear systems and there are relatively few results for nonlinear systems.As a kind of important nonlinear systems,PCH(Port Controlled Hamiltonian)system has abundant practical background,such as communication systems,mechanical systems and so on practical systems can be abstracted as the form of PCH system.Thus it is significant to solve the control problem about the saturated restriction of time-delay nonlinear systems under the framework of Hamilton system.In this paper,there are mainly about the nonlinear systems under the saturated restriction and studies two kinds of system input: constant time-delay and time-varying delay.It is well known that the immediate problem of stability analysis is how to design the controller to keep the closed-loop system stable in the presence of input saturation,delay and uncertainty.We mainly use L-K(Lyapunov Krasovskii)functional method and Wirtinger-inequality to get the less relatively conservative results.The main contents of this paper are as follows:(i)Stabilization of Hamilton systems with input constant delay and time-varying delay under saturation constraints.Firstly,the sufficient conditions for the stability of the Hamilton system with input constant delay is obtained by means of a special form of Wirtinger inequality.Secondly,due to the complexity of time-varying delay,we introduce another form of Wirtinger inequality,and then obtain the sufficient conditions for the stability of the system.Finally,the results are applied to the power systems to verify the correctness of the conclusions.(ii)Robust stabilization of uncertain Hamilton systems with saturating input delays.In this section,we consider the systems with non parametric uncertainties,which is belongs to a convex bounded polyhedral domain.Then,based on the Convex Combination method to deal with the saturation of the systems.Finally,the stability results of non parametric uncertain Hamilton systems with saturated input delays will received.Ultimately,a numerical example is given to verify the correctness of the results.