Research On Multi-rate Robust Stabilization And State Estimation Of Singularly Perturbed Systems

The progress of science and the development of network computing have made a mushroom growth,scholars have found that many practical chemical production processes,theoretical circuit systems and machine control models can be expressed by higher-order ordinary differential equations with perturbation parameters.According to the further study of this kind of control system,it is found that the perturbed parameters often leads to the increased dimension and stiffness of the system,making the system have multi-time scale characteristics.Nowadays,under the background of digital control,using the sampled-data control technique to cope with the numerical ill-conditioning problem which is due to perturbation parameters has become a common topic.Therefore,with combining the properties of multi-time scale and discrete output,it is of significant to discuss the impact on perturbation parameters on system control and ensure system to keep good control performance in a certain range of sampling periods.Based on the research status of singular perturbation system,this thesis mainly focus on the following aspects: the robust stability of singularly perturbing system based on multi-rate sampling feedback mechanism,impulsive observer-based design for state estimation of a class of nonlinear singularly perturbed systems with discrete measurements,and the state estimation problem of nonlinear singularly perturbing system based on sampled-data observer.To sum up,the main contents and contributions include:(1)The stability of linear singularly perturbed systems under a composite multi-rate sampled-data control is studied.In this thesis,a composite asynchronous sampled-data control mechanism is designed for multi-timescale characteristics.In particular,it is different from the pervious design ideas,the sampling times of the slow and fast state variables are allowed to be asynchronous and non-uniformly spaced.A new time-dependent Lyapunov functional is presented and the stabilization of closed-loop system is to be analyzed with the Young inequality and constant variation formula.It is useful to prove the exponential stabilization of the considered system.According to the Lyapunov functional and the linear matrix inequalities,a sufficient condition for the exponential stabilization can be derived.Moreover,this thesis also considers the case of uncertain singular perturbation parameter,and obtains the robust stability condition of close-loop system with the proposed composite asynchronous sampled-data control law.The effectiveness of the developed methodology is shown by the numerical examples.(2)The state estimation problem of a class of nonlinear singularly perturbed systems with discrete measurements is investigated.By making the assumption the states of fast dynamics are linear and exponentially stable.Under this assumption and some additional conditions,an asymptotic representation of the fast state is obtained according to the slow state and the known input.Then full state estimation problem reduces to slow state estimation problem.In terms of this observation,an impulsive observer based estimation scheme is presented.The continuous part of the proposed impulsive observer is a copy of the reduced-order slow dynamics of the observed system,while the impulse part is responsible for the implementation of the sample-triggered update of the observer state whenever a new sample of the output arrives.The estimation error is analyzed via a discontinuous Lyapunov function,and an ?-independent observer gain is designed.It demonstrates that the resulting estimation error exponentially converges towards an ultimate bound of order O(?).A numerical example shows that the proposed estimate scheme can achieve a desirable estimation accuracy for small enough ? > 0.(3)The design of sampled-data observer for a class of nonlinear singularly perturbed systems with discrete measurements is addressed.The closed-loop system with hybrid characteristics is obtained by introducing the reduced-order sampled-data observer.For the error system with hybrid characteristics,by constructing a time dependent Lyapunov function and using convex combination technique,the exponential stability criterion of the estimated error system is obtained,and estimation error exponentially converges towards an ultimate bound of order O(?).Finally,a numerical example shows that using impulsive update strategy to deal with state estimation problem based on continuous-discrete time observation can reduce the conservatism of the closed-loop system more effectively.