Abstract
This paper addresses a mean square exponential stability problem for a class of switched stochastic systems with time-varying delay. The time delay is any continuous function belonging to a given interval, but not necessary differentiable. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, new delay-dependent sufficient conditions for the mean square exponential stability of switched stochastic systems with time-varying delay are first established in terms of LMIs. Numerical example is given to show the effectiveness of the obtained result. MSC:15A09, 52A10, 74M05, 93D05.
Highlights
In the past decades, the problem of stability for neutral differential systems, which have delays in both their state and the derivatives of their states, has been widely investigated by many researchers
In [ – ], which are not based on the method of Lyapunov functional, one of them uses the diagonal equations for reducing systems of delay differential equations to ones of integral equations and estimates the norms or spectral radii of corresponding integral operators obtained on the basis of the results in the book
By constructing a Lyapunov functional combined with the LMI technique, we propose new criteria for the mean square exponential stability of switched stochastic systems with interval time-varying delay
Summary
The problem of stability for neutral differential systems, which have delays in both their state and the derivatives of their states, has been widely investigated by many researchers. This paper gives the improved results for the mean square exponential stability of switched stochastic systems with interval time-varying delay. By constructing a Lyapunov functional combined with the LMI technique, we propose new criteria for the mean square exponential stability of switched stochastic systems with interval time-varying delay. ) is α-exponentially stable in the mean square if there exists a switching rule γ (·) such that every solution x(t, φ) of the system satisfies the following condition:. The following is the main result of the paper, which gives sufficient conditions for mean square exponential stability problem for a class of switched stochastic systems
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