Research On The Reachable Set Boundary Of Neutral Markovian Jump System

Neutral Markov jump systems are a special class of switched systems with time-varying neutral delays.The boundary estimation of reachable set for such systems is one of the important properties of dynamic theory,and it is also a research hotspot of dynamic properties.In this paper,we mainly study the reachable set boundary problem of neutral Markov jump systems,including the reachable set boundary problem of neutral Markov jump systems with bounded perturbations and time-varying delays The reachable set boundary problem of uncertain neutral Markov jump systems and the reachable set boundary problem of neutral Markov jump systems with bounded perturbations and distributed delays are studied:1.The reachable set boundary problem of neutral Markov jump systems with bounded perturbations and time-varying delays is studied.Firstly,the delay is divided into two different subintervals,and a new augmented Lyapunov functional is constructed.Combined with the linear matrix integral inequality method,the less conservative reachable set boundary of the neutral Markov jump system is obtained,and the boundary is a set of ellipsoids.The matrix toolbox of MATLAB is used to solve these linear matrix inequalities.Finally,numerical examples are given to show the effectiveness of the results,and the boundary of the reachable set is smaller than that in the literature.2.The problem of reachable set boundary of uncertain neutral Markov jump system with disturbance and time-varying delay's studied.By constructing the linear matrix inequality method,the reachable set boundary conditions of the system are obtained by combining matrix inequality technique and free weight matrix idea.Numerical examples show the effectiveness and superiority of our results.3.The problem of reachable set boundary for neutral Markov jump systems with bounded perturbations and distributed delays is studied.By constructing an appropriate Lyapunov function,the method of linear matrix inequality and the idea of free weight matrix are used to study and analyze the boundary problem of reachable set,and a conservative reachable set boundary condition is obtained.Finally,the effectiveness and correctness of the results are proved by numerical examples.