Robust Exponential Stability Analysis for Stochastic Systems With Actuator Faults Using Improved Weighted Relaxed Integral Inequality

In this paper, the problem of the exponential stability criterion for stochastic delayed systems with actuator failures is investigated via weighted relaxed integral inequality. A suitable Lyapunov-Krasovskii functional (LKF) candidate is adapted to derive the sufficient conditions that guarantee the exponential stability of the considered stochastic system. The main concerned problem is to estimate stronger upper bounds than the conventional ones for the integral terms induced through the derivative LKF. For this estimation process, combining the weighted integral inequality together with the reciprocal convex lemma, a new type of relaxed-based integral inequality is introduced to bound the integral term based on the weighted integral inequality. By making the use of derived inequality, the desired exponential stability conditions are established by means of linear matrix inequalities (LMIs). Lastly, the applicability and superiority of the proposed theoretical results over the existing ones are examined in virtue of numerical examples.