Study On Robust Control For Delta Operator Systems With Time Delays

The delta operator model also has the advantage of better numerical properties at high sampling rates than traditional discrete-time systems. The method can unify some previous related continuous and discrete systems into the delta operator systems framework. Therefore, there is important value in both theory studies and practical uses. Time delay is common phenomenon in practical control systems. Time delay as a source of instability and poor performance often appears in many dynamic systems, therefore, it is important to study of robust control on delta operator system with time delay and ucertainties.The dissertation are mainly on the study of the robust stability analysis, controller and filter design on the uncertain delta operator systems with time delays. The organization of this dissertation is as follows:In chapter two, based on some new Lyapunov-Krasovskill functional method in delta domain and LMI technique, the problem of robust H_∞state feedback control foruncertain fuzzy delta operator systems with time delays is considered. A new fuzzy state feedback controller is designed such that resulting closed-loop uncertain fuzzy deltaoperator system with time delays is robustly asymptotically stable and satisfies a prescribed H_∞performance level, which is in terms of linear matrix inequalities whichcan be solved numerically using Matlab Control Toobox.In chapter three, the problem of robust passive filtering problem of delta operator systems with delays. The aim is to design arobustly stable filter which guarantees that the error system is robustly stable and the passive gain from the noise signal to the estimation error is below a prescribed level. All results are presented in terms of linear matrix inequalities (LMIs) form. Numerical examples are given to illustrate the feasibility andeffectiveness of the developed technique.In chapter four, the problem of both robust H_∞filtering and delta operator systemswith time-varying delays and Markovian jump parameters. A wider class of parameteruncertainties than norm-bounded parameter uncertainties is described in this model. Sufficient conditions for the delta operator filter to satisfy prescribed H_∞performanceare given in terms of LMIs, which can stabilize the system and guarantee a prescribed H_∞performance on attenuation of all admissible parameter uncertainties. A numericalexample is given to illustrate the feasibility and effectiveness of the developed technique. Last but not the least, based on the Lyapunov-Krasovskii functional method in delta domain and LMI technique, we study the problem of robust stability for a class of discrete neural networks with time-varying delays and and Markovian jump parameters via delta operator approach. The model contains a wider class of parameter uncertainties than norm-bounded parameter uncertainties. The proposed results can unify previous related conclusions of the continuous and discrete neural networks with uncertainties. A numerical example is given to illustrate the feasibility and effectiveness of the developed technique.