Integral Inequality for Time-Varying Delay Systems and Its Application to Output-Feedback Control

International audienceThis chapter considers the stability and stabilization of time-varying delay systems. We develop some new integral inequalities which are proved to encompass the celebrated Jensen’s inequality. These technical tools allow to construct simple Lyapunov-Krasovskii functionals very efficient in practice. Notice that our procedure is coupled with the use of the reciprocal convexity result in order to reduce the conservatism induced by the LMI optimisation setup. The effectiveness of the proposed results is illustrated by an example extracted from the dynamics of machines chatter