Control And Filtering For Nonlinear Markov Jump Singularly Perturbed Systems

With the increasing complexity of industrial systems,more industrial systems tend to show multi-time scale characteristics.Singular perturbation theory plays an important role in the analysis and modeling of such systems,and relevant research is gradually in-depth.On the other hand,many systems not only show the property of nonlinearity,but change their structural parameters randomly due to environmental factors.It is also a hot field to apply the Markov jump theory to the modeling of such systems.Therefore,the combination of the two theories can greatly improve the accuracy of the system model,and has a certain practical value.Based on the Takagi-Sugeno(T-S)fuzzy model,the control and filtering issues of singularly perturbed systems with Markov-type parameters are considered in the network-based framework.The major works are as follows:(1)For a class of nonlinear fast sampling Markov jump singularly perturbed systems,the non-fragile control problem with the mixed H_?and passive performance is studied.Firstly,the T-S fuzzy model method is used to approximate the nonlinearity of the system.Considering that the controller may be affected by uncertainties and cannot be realized accurately,a random variable obeying Bernoulli distribution is introduced to simulate the uncertainties in the controller.Then,based on the Lyapunov stability theory and stochastic analysis theory,the stability of the system is analyzed,and the relevant criteria to ensure the stochastic stability of the system and the existence of the controller are obtained.Finally,a simulation example of the tunnel diode circuit is given to verify the feasibility of the design scheme.(2)For a class of nonlinear semi-Markov jump singularly perturbed systems,the quantized control of the system in the network-based framework is studied.Different from Markov jump systems,in order to reflect the information of sojourn time of the system in different modes more reasonably,the semi-Markov-type parameters related to the sojourn time are introduced to the system.Similar to the method used in(1),the T-S fuzzy model of the nonlinear system is obtained firstly.Then,considering the quantization effect of networked control system and the data packet dropout caused by network congestion,the controller model designed is described reasonably.According to the Lyapunov stability theory,the stability analysis is carried out to establish some criteria which can ensure the system to be mean square stable and the existence of the controller.Meanwhile,the design method can effectively improve the upper bound of the perturbation parameters.In the simulation,the DC motor model is used to prove the effectiveness of the designed controller,and the influence of different quantization densities and packet loss rates on the system are discussed in the examples.(3)For a class of nonlinear Markov jump singularly perturbed complex networks,the H_?filtering is studied.Since the modal information of the system is not entirely available for the filter in practice,the Hidden-Markov model is introduced to the design of the filter,which is based on a detection signal.In addition,due to the limitation of network bandwidth,the round-robin protocol is applied in the networks to optimize data transmission.Such a protocol can effectively avoid the data disorder and data packet loss.Then,through Lyapunov stability analysis theory,relevant stability criteria are obtained,and the specific expressions of filter gains are determined.Finally,a simulation example is used to verify the obtained filter.