Mean square stability of linear stochastic neutral‐type time‐delay systems with multiple delays

Abstract

This paper studies mean square exponential stability of linear stochastic neutral-type time-delay systems with multiple point delays by using an augmented Lyapunov-Krasovskii functional (LKF) approach. To build a suitable augmented LKF, a method is proposed to find an augmented state vector whose elements are linearly independent. With the help of the linearly independent augmented state vector, the constructed LKF, and properties of the stochastic integral, sufficient delay-dependent stability conditions expressed by linear matrix inequalities are established to guarantee the mean square exponential stability of the system. Differently from previous results where the difference operator associated with the system needs to satisfy a condition in terms of matrix norms, in the current paper, the difference operator only needs to satisfy a less restrictive condition in terms of matrix spectral radius. The effectiveness of the proposed approach is illustrated by two numerical examples.

Stabilization of highly nonlinear stochastic neutral Markovian jump systems with multiple delays

“…This section will show that it is possible to design a u(y(t − 𝛼), 𝛾(t ), t )(0 < 𝛼 < 𝜏) that makes the controlled HNSNMJS (27) AS and ES in the sense of p-th moment and almost surely.…”

“…Most of the existing results are for the case containing only one retarded derivative of the state. However, many practical systems have multiple time delays [26][27][28][29], which may bring about more complex instability, and undoubtedly makes the research much harder. Song et al [30] first explored the almost surely asymptotic stability of a class of HNSNMJSs with multiple delays, and they found that the stability of the system only depends on the delays of the drift term.…”

“…Let Assumptions 1-3 and condition (21) hold. The controlled HNSNMJS (27) with any initial data (2) has a unique global solution y(t ) on [−𝜏, ∞). In addition, the solution y(t ) satisfies ( 6), (7) and (22).…”

Reachable set estimation for neutral Markovian jump systems with mode‐dependent time‐varying delays

“…Remark In some engineering systems (eg, heat exchangers, distributed networks, and car‐like robots), time‐delay is encountered in both the states and their derivatives 31 . This promotes the scientific research on neutral time‐delay systems.…”

Delay‐dependent stability of nonlinear hybrid neutral stochastic differential equations with multiple delays

“…Shen et al studied the stability of the hybrid NSDDEs with highly nonlinear coefficients and they solved those systems with a single delay in Reference 20. However, lots of real systems have multiple time delay states (see, eg, References 23‐26). Therefore, we will further investigate the stability of the hybrid NSDEs with multiple delays, where their coefficients are highly nonlinear.…”