The Analysis And Control For Singular Time-delayed Systems With Markovian Jumping Parameters

Today, singular time-delayed systems has gained extensive research, delay segmentationmethod has become an effective way to deal with time-delay at the same time. Meanwhile,due to external random events disturbances and components damage, the systems’ structuretends to change. Markovian jumping system is a valid model for the above conditions. Inpractice, singular time-delayed systems with Markovian jumping parameters widely exist innetwork systems, electrical systems, biological systems, which provide a broad soil inpractical application. In theory, the study of singular time-delayed systems with Markovianjumping parameters is also an important direction about the study of complex systems. Thispaper study this question from three aspects. Firstly, considering the condition which exists inthe transfer rate of some unknown circumstances for singular time-delayed systems withMarkovian jumping parameters, this paper studies the stability analysis of the problem;Secondly, this paper studies the presence of uncertainty robust H∞guaranteed cost controlproblem with singular time-delayed systems with Markovian jumping parameters; Thirdly, westudy H∞control problem for a class of T-S fuzzy singular time-delayed systems withMarkovian jumping parameters. The contents are as follows:1. Based on the delay partitioning method, firstly, we studies the problem of stabilityfor a class of singular time-delayed systems with Markovian jumping parameters. Therecurrence is presented when the time delay is divided into n0parts. At the same time, we alsostudied the stability condition when the transition rates are unknown and gave a set of criteria.2. Secondly, it is concerned with delay-dependent robust H∞guaranteed cost control(RH∞GCC) problem for uncertain singular time-delayed systems with Markovian jumpingparameters. Firstly, in terms of the Layapunov-Krasovskii technique and delay decompositionapproach, a delay-dependent bounded real lemma which ensures the considered systems H∞performance index stochastically admissible is established, then a corollary of thisdelay-dependent bounded real lemma is got. Nextly, based on this corollary, the sufficientconditions are obtained for the existence of H∞guaranteed cost controller, which guaranteesthe closed-loop systems of uncertain singular time-delayed systems with Markovian jumping parameters are not only stochastically admissible, but also have H∞performance index andthe quadratic cost function smaller than an upper bound. The explicit expression of controlleris characterized by solving asset of LIMs. Lastly, Numerical examples are given to show lessconservativeness and effectiveness.3. Lastly, it is concerned with H∞control problem for T-S Fuzzy SingularTime-Delayed Systems with Markovian Jumping Parameters. Firstly, in terms of theLayapunov-Krasovskii technique, a delay-dependent sufficient conditions which ensures theconsidered systems H∞performance index stochastically admissible is established. Secondly,throuth the matrix transform, a delay-dependent sufficient condition is obtained at the form oflinear matrix inequality. The explicit expression of fuzzy state feedback controller ischaracterized by solving asset of LIMs. Lastly, Numerical examples are given to show theeffectiveness.4. For above all, this paper has specific numerical examples and simulation. Throughsimulation examples, this paper shows the effectiveness and superiority.