| Markov jump systems is simple in mathematical form and suitable for modeling the actual system.As a result,much attention from domestic and foreign scholars has been paid to the study of Markov jump systems.The results obtained have been widely applied to engineering fields,such as power systems,communication systems,aircraft control,etc.Dissipative theory plays an important role in the study of system stability.Essentially,there is a nonnegative energy function,and the supplied energy from outside the system is greater than the increase in energy storage inside the system.The dissipative theory can establish the relationship.between some mathematical tools and physical phenomena.Thus,it has theoretical basis and application value to analyze the markov jump system through the dissipative theory.In this thesis,by means of some summation inequality,the stability of the system is analyzed,and the suitable controller or filter is obtained.The main work are concluded as follows.(1).A mode-independent filter is presented for a class of distributed Markov jump systems subject to randomly occurred uncertainties.Due to the existences of modeling error,a random variable which is subject to a Markov chain is introduced to govern the jumping uncertainties.Considering the unreliable channels between the system and filters,a discrete-time fading model is introduced to describe this channel fading phenomenon with the discrete probability distribution of each channel coefficients known a priori.On the basis of a fixed network topology,we make full use of available information to estimate the signal of the system.(2).The stabilization problem is studied for a class of Markov jump systems with with time delay.To reduce the conservatism of the result obtained,we adopt a mode-dependent and delay-dependent Lyapunov function.Through the recourse some summation inequal-ity,a dissipative controller or filter is designed which can ensure the stability and dissipa-tivity of Markov jump systems.(3).The problem of asynchronous filtering for T-S fuzzy Markov jump systems sub-ject to randomly occurred quantization is considered.Considering the random fluctuations of network conditions,the randomly occurred quantization is introduced to overcoming the contradiction between transmission information and limited bandwidth.To take full advan-tage of partial information of system modes for the desired system performance,we adopt the asynchronous filter in which mode transition matrix is nonhomogeneous.The gains of the filter are obtained by solving a set of linear matrix inequalities.(4).The problem of asynchronous filtering for nonlinear systems subject with nonuni-form sampling.To facilitate analysis,a discrete-time Takagi-Sugeno fuzzy model with a fast and uniform period is introduced to approximate continuous nonlinear systems.A slow and nonuniform sampler between system and filter is proposed to overcome the con-tradictions between fast sampling period and limited bandwidth.The nonuniform sampling interval of sampler is subject to a Markov chain.To make full use of the partial informa-tion of sampling interval which is accessible to the filter,the asynchronous filter which is described by the hidden Markov model is introduced to reduce conservatism.(5).An asynchronous and resilient filter is proposed for Markov jump neural net-works subject to extended dissipativity.Due to the fluctuation of the filter parameters,a resilient filter taking into account parameter uncertainty is adopted.Being different from the norm-bound type of uncertainty which has been studied in a considerable number of the existing literatures,the interval type of uncertainty is introduced so as to describe un-certain phenomenon more accurately.Considering the limited computing power of Matlab solver,a relatively simple simulation is exploited to verify the effectiveness and merits of the theoretical findings where the relationships among optimal performance index,uncer-tain parameter,and asynchronous rate are revealed. |
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