Study On Control And Filtering Of Parameter-Switching Repeated Scalar Nonlinear Systems

Nonlinear systems are common in practical applications.Repeated scalar nonlinear systems can be represented by state space equation,in which the same nonlinearity can be described by every sate sub-vector,providing an approach to the analysis and synthesis of multi input and multi output nonlinear systems with simple structure.However,due to the complexity,there exist many limits in the general form of repeated scalar nonlinear systems with complex nonlinearity and uncertainty.Also,it brings some difficulties to controller design and filtering.Now,when dealing with complex nonlinearities and uncertainties,switched systems can describe the complex nonlinear systems well.Since they consist of a series of continuous/discrete subsystems with corresponding switching sequence,the switched systems can describe a wide class of hybrid systems.Therefore,based on the advantages of switched systems,a category of switched repeated scalar nonlinear systems have made great progress.However,it is worth noting that the analysis and synthesis of the above systems are not studied adequately.Although some results concerning controller design and filtering have been published,there exist space to improve those results.In this thesis,considering the characteristics of repeated scalar nonlinear systems,and using switching theory,the model of such systems are established.And then,the conditions to controller design,filtering and fault detection are developed.Meanwhile,we apply the proposed theoritical results to the underactuated manipulators,solving the fault detection problem.This thesis aims to propose a series of effective approaches to analysis and synthesis of repeated scalar nonlinear systems.The main contents,novel techniques and original theoretical contributions of this thesis are presented as follows:1.Constructing a switching-sequence dependent Lyapunov function with the positive definite diagonally dominant matrix technique,sufficient conditions are developed to guarantee the closed-loop system is asymptotically stable with H?performance.Moreover,the sufficient criteria to design the state-feedback controller are established to ensure the considered system satisfies the predefined performance.2.By combining the switching-sequence dependent Lyapunov function technique with the positive definite diagonally dominant matrix technique,a sufficient stability condition with less conservativeness is firstly proposed,which guarantees for the concerned switched systems with repeated scalar nonlinearities to be asymp-totically stable with a prescribed H?disturbance attenuation performance.Then the desired full-order output feedback controller is designed by using projection approach.Due to the involved matrix equalities in the obtained conditions,the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities,which can be readily solved by using standard numerical software.3.Our attention is focused on the design of full-and reduced-order filters that guarantee the filtering error system to be stochastically stable with a prescribed weighted ?2-??performance.By employing both the mode dependent Lyapunov function approach and the positive definite diagonally dominant Lyapunov function technique,a sufficient condition is firstly established,which guarantees the Markovian jump repeated scalar nonlinear system to be stochastically stable with an induced?2-??disturbance attenuation performance.The corresponding full-order filter design is cast into a convex optimization problem.4.To reduce the overdesign of the quadratic framework,this paper proposes a switchingsequence dependent Lyapunov function approach to the fault detection filter design procedure.Sufficient conditions are obtained for the existence of admissible generalized H2 fault detection filter.Since these conditions involve matrix equalities,the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities(LMIs),which can be readily solved by using standard numerical software.If these conditions are feasible,a desired fault detection filter can be easily constructed.5.The purpose is to design a fault detection filter for underactuated manipulators such that the filtering error system is stochastically stable and the prescribed probability constraint performance can be guaranteed.The existence conditions for a fault detection filter are proposed through the stochastic analysis technique,and a new fault detection filter algorithm is employed to design the desired filter gains.In addition,the cone complementarity linearization procedure is employed to cast the filter design into a sequential minimization problem.