Research On Several Classes Of Control Problems For Affine Nonlinear Singular Systems

Singular systems are a natural representation of objective systems and they describe a class of dynamic systems which are more widespread than the normal systems. In general, the controllers design for nonlinear singular systems are more difficult, and accordingly, there are fewer results on nonlinear singular systems except for several special cases. In recent years, differential geometry theory and adaptive control theory have been widely applied to nonlinear singular systems and achieved many important works.This paper studies several classes of control problems for affine nonlinear singular systems, using linear matrix inequality(LMI) method,the Lyapunov stability theory and M derivative. The main contents of this paper as follows:(1) The state feedback control problem is studied for a class of affine nonlinear singular systems. Firstly, the affine nonlinear singular systems are transformed into linear parameter-varying singular systems via differential mean value theorem(DMVT). Then based on LMI method and the Lyapunov stability theory, one state feedback controller and another which is constructed with state observer is designed separately, meanwhile, sufficient conditions under which the systems are asymptotically stable and errors are asymptotically convergent are given. The results of simulation show that the effectiveness of the presented method.(2) The parametric adaptive control problem is studied for a class of affine nonlinear singular systems with unknown parameter. Based on parametric adaptive control method combined with LMI method and the Lyapunov stability theory, a adaptive regulator is constructed and a sufficient condition is given under which the system is asymptotically stable at the point of equilibrium and parameter error is asymptotically convergent. The results of simulation show that the feasibility of the presented method.(3) The disturbance decoupling control problem is studied for a class of Multiple-Input Multiple-Output(MIMO) affine nonlinear singular time-delay systems by differential geometry theory. Based on M derivative, nonlinear state feedback controllers and local diffeomorphism transformation are constructed, meanwhile, sufficient conditions under which systems can realize disturbance decoupling are given. Numerical example proves that the correctness of the presented method.