## New results on stability analysis for systems with discrete distributed delay.(English)Zbl 1331.93166

Summary: The integral inequality technique is widely used to derive delay-dependent conditions, and various integral inequalities have been developed to reduce the conservatism of the conditions derived. In this study, a new integral inequality is devised that is tighter than existing ones. It is used to investigate the stability of linear systems with a discrete distributed delay, and a new stability condition is established. The results can be applied to systems with a delay belonging to an interval, which may be unstable when the delay is small or nonexistent. Three numerical examples demonstrate the effectiveness and the smaller conservatism of the method.

### MSC:

 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93C15 Control/observation systems governed by ordinary differential equations 93D30 Lyapunov and storage functions
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### References:

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