This paper discusses an H∞ control problem as observer-based delay-dependent stability of time-varying stochastic systems represented by Linear Parameter Varying (LPV) description. For the control problem, the integral delay terms in the derivatives are dealt with a proposed novel extended reciprocal convex inequality. Based on the proposed inequality, some extra matrices are created to decrease the conservatism of the developed stability criterion. Furthermore, a Lyapunov-Krasovskii Function (LKF) possessing a parameter-dependent positive definite matrix and the integral term is utilized for the stability criterion. Besides, an additive inequality is proposed to constrain the bounds of the state and estimated error to the external disturbance for achieving H∞ performance. Through the proposed lemma, the indexes for the state and the error can be individually assigned to avoid the high-gain response. Based on the convex calculation, the proposed criterion can be directly utilized to design an observer-based controller so that the delay-dependent stability and H∞ performance of the closed-loop system is achieved. And then, some numerical simulations are used to show the contributions of this paper.
