Mean square exponential stability of uncertain singular stochastic systems with discrete and distributed delays

Abstract

The problems of exponential stability for a class of the uncertain singular stochastic systems with discrete and distributed delays are studied. By using a Lyapunov–Krasovskii functional approach and terms of linear matrix inequalities (LMIs) and the Leibniz–Newton formula, mean square exponential stability criteria ensuring robust stability of the uncertain singular stochastic systems with discrete and distributed delays are established. New mean square exponential stable criteria for the certain singular stochastic systems with discrete and distributed delays are obtained as well. Finally, the validity of the obtained results is shown by a numerical example.

Keywords:

• Stochastic systems
• Singular systems
• Lyapunov–Krasovskii functional approach
• Linear matrix inequalities
• Discrete and distributed delays