The Stablity Analysis And H_∞Controller Design Of Sampled-data Control Systems With Time-varying Delay

With the development of computer technology, computer control and digital control technologyhave been widely used for industrial control systems, to control the continuous time object by adigital computer, as the sampled-data controller. What’s more, for social, economic, and biologicalsystems, the relevant information are often collected by discrete methods, and the useful signals aresampled for a feedback control system. Therefore, sampled-data control systems (SDCSs) havebeen widely used, and research on the theory of SDCSs has great practicality. In recent years,sampled-data control systems have received widespread attentions. However, under the influence ofthe time-delay, the uncertainty and external disturbance factors in systems, there is always a gapbetween theoretical results and engineering practical results, ie. the theoretical results are alwaysconservative. This kind of conservativeness in results is because of the incomplete modeling for theclosed-loop system, or the insufficient dynamic characterization for the sampled-data controlsystems by the construction of Lyapunov functionals, or the reason is that the functional derivativeunable to be carried out effective and appropriate definition. Thus, in order to minimize or eveneliminate this conservativeness, and to improve the results’ versatility, the study of the sampled-datacontrol systems is necessary. This paper mainly deals with the research of stability analysis and H∞controller design problems for the sampled-data control systems with time-varying delay andparameter uncertainties.Firstly, this paper gives an overview of the sampled-data control systems and some relatedissues, such as: the stability problems for the sampled-data control systems with delays, the robustcontrol problems for the systems with uncertainties, cone complementarity linearization algorithmissues. Such problems’ research is analyzed, and the advantages and disadvantages of the existingresults and methods are summarized. And the corresponding introduction about the backgroundknowledge and theoretical foundation for sampled-data control systems is made.Secondly, in the third chapter, based on some results of previous studies, take advantage of theinput delay method. By using the input delay method, that is to say, a time-varying delay isartificially constructed into the input signal of the state feedback sampled-data controller, totransform the system into closed-loop control system with piecewise continuous input delay. Andbased on the Lyapunov stability criterion, we construct an appropriate Lyapunov function,considering those usually ignored integral terms, defining the cross-term appropriately. What’s more,the information of the state delay of the system and the information of the artificial introduced delayhave been taken into account. And then we can get the less conservative delay-dependent bounded real lemma for the sampled-data control systems with time-varying delay.And then we proposed the modified cone complementarity linearization algorithm (CCLA) forsolving nonlinear matrix inequalities, and a good scheme to get parameters for the controller hasbeen put forward, based on the previously obtained delay-independent bounded real lemma.Through the modified CCLA algorithm, the controller design problem is transformed intooptimization problem with LMIs constraint conditions, and the sufficient conditions which have afeasible solution for the controller parameter K have been expressed in the form of LMIs. Themodified CCLA algorithm reduces the number of the matrix variables introduced, thus reducing thecomputational complexity of the iterative algorithm, respect to the traditional CCLA algorithm. Theiterative algorithm is given to obtain feasible solution of the H∞controller parameter, whichsatisfing the controller design requirements.Further considerating the norm-bounded uncertainties which affect both the system stability andcontrol performance, the robust stability analysis and the robust H∞control problems for theSDCSs with time-varying delay and parameter uncertainties are discussed in the fifth chapter, basedon the bounded real lemma and method for the H∞controller design obtained in the previous twochapters. Using the input delay method to design the robust H∞controller, a variable input delay isartificially constructed into state feedback sampled-data controller, and the information of the statedelay and the information of the artificial constructed input delay have been taken into account forconstructing Lyapunov function, so the results can be less conservative. With the lemma related tothe processing of parameter uncertainty, the delay-dependent bounded real lemma and conditions innonlinear matrix inequality for existence of the robust controller, which satisfying not only therobust asymptotic stability of the system, but also the performance index, is obtained. The previousmodified CCLA algorithm is used to simplify the matrix inequalities and reduce the computationalcomplexity of the traditional algorithm，while solving nonlinear matrix inequality to achieve thefeasible solution; The specific steps of iterative algorithm to get the maximum sampling period andthe robust H∞controller parameter K, is presented.Finally, through numerical examples of the systems, results of tables and graphics are obtainedby MATLAB programming and simulink, to verify the effectiveness and correctness of theproposed method.