Resarch On Robust Stability Of Uncertain Discrete-time Systems With Time-delays And State Saturation

Due to the rapid increase of the applicability of the modeling method inpractical engineering systems, the dynamic system models which are used todescribe the actual situations become more complicated. The related systemmodels are considered many external factors such as delay, uncertainty, externaldisturbance, saturation nonlinearity, and random variable, ect. The problems ofthe stability analysis and control have attracted considerable attention for a classof the complex systems. However, due to the increase of the system complexity,many established theories and methods are found to be inadequate. Therefore,the new methods and techniques are extensively developed and successfullyapplied in practical engineering systems. The stability problem is investigatedfor a class of complex discrete dynamic systems with both time-delays anduncertainties and state saturation nonlinearities. By applying Lyapunov methodand matrix inequality technique and delay-fractioning approach, the newcriterion of the robust stability is obtained.Firstly, the robust stability problem is discussed for a class of discrete-timeuncertain systems with multi time-delays and state saturation nonlinearities. Thedelays are allowed to be time-varying but bounded functions, and theuncertainties are allowed to be norm-bounded uncertainty, and the statesaturation nonlinearities are assumed to be standard saturation functions. It isworth mentioning that the construction of the new discrete-time Lyapunov-Krasovskii functional has taken full effects from time delays. By combining thefeature of state saturation nonlinearity, the matrix variable and a non-negativescalar are introduced. Then, a delay-dependent sufficient condition for globalrobust asymptotic stability is presented by applying discrete-time Lyapunov stability theory and matrix inequality method for dealing with norm-boundeduncertainties. The obtained results are generalized and improved. Secondly, thesingle time-delay case is discussed extensively for the systems. By constructingthe discrete-time Lyapunov-Krasovskii functional with delay-fractioninginformation, the delay-dependent sufficient condition of the robust globalasymptotic stability is obtained for discrete-time uncertain systems with singletime-delay and state saturation nonlinearities. It concludes that the stabilitycondition in this paper is less conservative than the other one. Finally,comparative analysis and the numerical example are given to show theeffectiveness of the presented criterion.