Nonstationary Filtering Design Of Markov Jumping System

Markov jumpinp system is a special kind of hybrid system.Its mathematical form is simple and suitable for describing the random disturbance in the actual control system,which greatly enriches the control system theory.It is used in aerospace,communications,industrial manufacturing,medical treatments.There are extensive researches in areas such as electric power.Although the Markov jumping system has achieved good results in many fields,there are still many random phenomena,such as packet loss,signal delay and so on,which make signal strength and density of the actuator and sensor are nonstationary,,so this also tests the signal processing ability of the system filters(controllers).In order to reduce control costs and meet the needs of actual industrial applications,it is necessary to design filters(controllers)that are more sensitive to nonstationary signals.To enhance the adaptability and adjustability of the control system.In this thesis employs the Markov jumping system to describe several common random phenomena in the actual control environment,and proposes a nonstationary filter design method.The characteristic of this filter is that it has multiple filter modes that follow Markov transition probability,including one filter mode synchronized with the system and multiple asynchronous filter modes.The purpose of this design is to not only obtain system modal information,but also make full use of other abnormal system modal information caused by random phenomena.And it can be transformed into a modal independent filter,a modal synchronous filter or an asynchronous filter through parameter degradation,which has strong adaptability and adjustability to deal with the nonstationary system operating environment.The main research content of this thesis can be summarized as follows:Research the filtering problem of Markov jumping system with nonlinear repeated scalar.In the establishment of the system model,irrelevant random variables are introduced to describe the noise disturbance Brownian motion in the actuator and the random nonlinear phenomenon in the sensor.On the basis of obeying Lyapunov's stability theory,the nonstationary l₂-l_? filter is designed to ensure the stochastic stability of the closed-loop system and suppress the interference.Finally,the gain of the filter is obtained by solving the matrix inequality,and the trajectory of the whole closed-loop system is shown through the simulation example,which clearly reflects the feasibility of the proposed nonstationary filter.(1)Research the filtering problem of Markov jumping system with fading channels,which the multiplicative noise existing in the sensor and the controller,At the same time,the range of variables in which Brownian motion occurs in the sensor are expanded.Combined with the properties of diagonally dominant matrix,the Lyapunov function is determined,and the sufficient conditions of stochastic stability and l₂-l_? jamming suppression ability of closed-loop system are given.Finally,through a simulation example,the performance of the nonstationary filter and the traditional asynchronous filter are compared and analyzed,which shows that the nonstationary filter has better adaptability,can make the system stable more efficiently and quickly,and get less conservative running results.