Compound Anti - Jamming Control For Multi - Interference Markovian Jump Nonlinear Systems

Disturbances exist in the practical system with various forms, and seriously influence the performance of these systems. With the requirement in high performance control, the ability of anti-disturbance of system should be enhanced. Moreover, due to the practical background of Markovian jump non-linear systems, it has received widespread attentions from many experts in recent years. In this paper, the problem of composite anti-disturbance resilient control is studied for Markovian jump nonlinear systems, and some new results have been obtained. The main results are given as follows:（1）. The problem of composite anti-disturbance resilient control is studied for Markovian jump nonlinear systems with multiple disturbances. The multiple disturbances include two types:one is in the input channel generated by an exogenous system with perturbations, and the other is belong to L2[0, ∞). A disturbance observer is established to estimate the disturbance generated by the exogenous system. Based on the value of disturbance estimation, a composite anti-disturbance resilient controller is structured. Then, some sufficient conditions are given by Lyapunov stability theory and linear matrix inequalities technique to guarantee the closed-loop system stochastic stability with L₂-L_∞performance. Finally, an application example is given to illustrate the effectiveness of the proposed approach.（2）. The problem of composite anti-disturbance resilient control is studied for Markovian jump nonlinear systems with partly known transition rates under multiple disturbances. Under the case of partly known transition rates, some sufficient conditions are obtained by using Lyapunov function method and linear matrix inequality technique. Finally, an application example is given to illustrate the effectiveness of the proposed approach.（3）. The problem of composite anti-disturbance resilient control is studied for Markovian jump nonlinear systems with general uncertain transition rate under multiple disturbances. Based on this case, a sufficient condition is obtained such that the closed-loop system is stochastically stable with L₂-L_∞performance. Moreover, the gains of the resilient controller and the observer are acquired by applying linear matrix inequalities technology. Finally, an application example is given to illustrate the effectiveness of proposed approach.（4）. The problem of composite anti-disturbance resilient control is addressed for time-varying delay Markovian jump nonlinear systems with multiple disturbances. For the time-varying delay Markovian jump nonlinear systems, some sufficient conditions are given by Lyapunov stability method and linear matrix inequalities technique to guarantee the closed-loop system stochastic stability with L₂-L_∞performance. Finally, an application example is provided to demonstrate the effectiveness of the proposed method of the main algorithm.（5）. The problem of composite adaptive anti-disturbance resilient control is investigated for Markovian jump systems with partly known transition rate and multisource disturbances. The considered multisource disturbance are included three parts: the first is a single of harmonic or constant disturbance, the second is an unexpected nonlinear signal which is described as a nonlinear function and uncertain parameter, and the last one is supposed to be bounded H2 norm.Based on the composite adaptive anti-disturbance resilient controller, some sufficient conditions are present in terms of linear matrix inequalities such that the closed-loop system is stochastically stable with L₂-L_∞performance. Finally, simulations for a numerical example and an application example are given to illustrate the effectiveness of proposed approach.