Disturbance Decoupling Problems With Stability Of Singularly Perturbed Systems

In this thesis,the solvability of the disturbance decoupling problems with stability(DDPS)for linear singularly perturbed control systems(SPCSs)is studied.The characteristic of the traditional singular perturbation method is based on DDPS of the limiting systems(under standard condition of SPCSs,it is composed of two parts of slow-fast subsystems)to obtain DDPS of the whole SPCSs by Lyapunov method.Due to the conditions of DDPS are involved in the concepts of(A,B)-invariant-subspaces,there exists a big technical obstacle to keep the(A,B)-invariance in the whole space caused by the errors by the method of enlarging inequalities in Lyapunov method.Therefore,it is not applicable to study DDPS of SPCSs by the traditional singular perturbation method.We will use a limiting preservation method instead to study the solvability of DDPS of linear SPCSs in this thesis.It is effective to avoid the difficulty caused by the traditional singular perturbation method in this study.In this thesis,we have done in this regard for three different classes of problems as follows:1.The solvability of DDPS for linear SPCSs.2.The solvability of disturbance decoupling problems(DDP)for linear SPCSs.3.The system structure demanded on solvability of DDPS(DDP)for linear SPCSs.Firstly,we regard the linear SPCSs as the parameterized systems with small parameters to deal with the corresponding DDPS.On the basis of the parameterized DDPS,we study the limiting preservation of the DDPS as ε→0 to obtain the corresponding limiting preservation conditions so as to get the conditions such that DDPS is solvable(i.e.it is strong DDPS).It is noticed that those conditions are dependent on parameter,which is not convenient to be verified.We expect to obtain the conditions independent of parameter.This is one difficult and key point by using the limiting preservation method.In this thesis,we obtain the sufficient conditions on the solvability of DDPS by mathematical constructive way,which are independent of parameter.An example shows the effectiveness on the obtained criterion conditions for the solvability of DDPS.Secondly,we study the solvability of DDP for the linear SPCSs.Since there is a close connection between the solvability of DDPS and DDP,we obtained a series of results on the solvability of DDP for SPCSs without the demand of pole stability for DDPS.Finally,we study what system structures naturally have to guarantee solvability of DDPS or DDP.