Finite-Frequency Robust Synthesis Based On Polynomially Parameter-Dependent Technique

In practice engineering,model uncertainty arises from a variety of sources,such as variation of operation point,external disturbances,unmodeled dy-namics and aging of the components.Typically,many actual signals such as seismic waves,atmospheric turbulences reside in certain frequency ranges.Meanwhile,practical requirements should be satisfied in restricted frequency ranges,e.g,the tracking performance in the low-frequency interval and the noise-attenuation performance in the high-frequency range.Therefore,it is of theoretical significance and practical value to study the problem of finite-frequency robust synthesis.Based on previous works of others,this thesis,in the framework of the polynomially parameter-dependent approach,system-atically investigates the problems of performance analysis.controller design,filtering and estimation,and presents analysis and synthesis methods for un-certain systems.To be specific,sufficient conditions for the existence of ro-bust controllers and robust filters are established via the generalized KYP lemma and homogeneous polynornially parameter-dependent(HPPD)tech-nique,which reduce the conservatism of the existing methods,thus improving the control and filtering performance.The main contents of this thesis include the following aspects:1.Chapter 3 investigates the robust controller design for polytopic uncer-tain linear systems disturbed by external disturbances in restricted frequency ranges.A robust generalized KYP lemma is applied to describe the finite-frequency specification,aiming at improving the disturbance-attenuation per-formance over the given frequency range.In this setting,more relaxed analysis conditions for robust stability and finite-frequency specifications are derived by introducing additional slack variables,which contain some existing condi-tions as special cases.Based on the HPPD technique,new controller design conditions in terms of matrix inequalities are developed.On this basis,we pro-pose an iterative algorithm to solve and optimize the controller gain,which is illustrated by an example about the satellite system.2.Chapter 4 proposes a new solution to static output-feedback(SOF)control for a class of linear uncertain systems with disturbances in restricted frequency intervals.In order to strengthen the disturbance-rejection capability over the given frequency range,we firstly establish sufficient and necessary analysis conditions via the generalized KYP lemma,under which the HPPD technique is adopted to reduce conservatism.Then,the issue of SOF controller design boils down to solving constrained optimization problems subject to bilinear matrix inequalities(BMIs),which is a typical NP-hard problem.To get out of the predicament,we propose a more relaxed convex feasible set to approximate the original one,based on which a local optimization algorithm is developed and its convergence is analyzed.Finally,an active-suspension system is given to demonstrate the efficiency of the results.3.Chapter 5 studies the dynamic output-feedback control(DOF)for discrete-time poly topic uncertain systems.Firstly,we formulate the problem of dynamic output feedback control as a static output-feedback control for the augmented system,which enables us to utilize the results in Chapter 4.More-over,an iterative algorithm for the initial value optimization was proposed due to the fact,that as a heuristic algorithm,the efficiency of the sequen-tial convex optimization algorithm is highly affected by the initial solutions.The advantages of the proposed design method is finally demonstrated by the application to active control of suspension systems.4.Chapter 6 investigates the problem of robust filtering for continuous-time linear uncertain systems affected by external noises in finite-frequency ranges.Firstly,the product terms between the Lyapunov matrices and the filter parameters are decoupled by introducing additional slack variables,and it is shown that the proposed analysis conditions encompass the existing results by employing particular choices of slack variables.By the aid of the HPPD technique,we present less conservative filter design conditions.On this basis,a successive approximation strategy is used to apply the current optimal solution to the next iteration.aiming to improve the filtering performance.Finally.an example about F-18 aircraft model is given to illustrated the effectiveness of the proposed method.5.Chapter 7 considers the finite-frequency memory filter design prob-lem for discrete-time systems with polytopic uncertainties.Different from the traditional filter schemes,a finite-frequency memory filter is designed to gen-eralize conventional memoryless ones in such a way that a sequence of latest output measurements is employed for current estimation.By the generalized KYP lemma,a memory filter is sought which ensures that the extended filter-ing error system is asymptotically stable with a prescribed noise-attenuation level in the restricted frequency range.Moreover,the polynomially parameter-dependent Lyapunov matrices are adopted to facilitate filter design and reduce conservatism.It is proved rigorously that additional past output measure-ments contribute to less conservative results.Finally,a quarter-car model with an active-suspension system is used to validate the proposed scheme.