A note on Wirtinger-type integral inequalities for time-delay systems

Improved delay‐range‐dependent stability analysis for uncertain retarded systems based on affine Wirtinger‐inequality

“…In this note, improved delay‐range‐dependent stability condition for a general class of uncertain or nonlinear retarded system is derived using recently proposed affine Wirtinger inequality in with appropriate Lyapunov–Krasovskii function (LKF). According to authors, no work on robust stability of generalized class of uncertain or nonlinear retarded system has been reported so far utilizing affine Wirtinger inequality.…”

“…In past decades, vast literature on improvements of bounding inequalities as well as appropriate choice of L-K functional to fit the usage of bounding inequalities have been reported with an objective to enhance the result of delay upper bound. A detailed chronological review on improvement of the delay upper bound results by developing new methods can be found in [3] and more recent developments can be found in [4,[7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references there in validating the fact that this field of research is still treated as an open problem in computation and control field (see e.g. [3,5] and references therein).…”

H∞ Control of Coronary Artery Input Time-Delay System via the Free-Matrix-Based Integral Inequality

“…It is well known that the stability and synchronization of the considered systems with time 2 Mathematical Problems in Engineering delay are often studied by introducing the LKF method, which can provide more useful state information and delay information. In order to reduce the possible conservatism of LKF method, many methods are proposed, such as the Jensen inequality [17], Wirtinger inequality [18], and freematric-based integral inequality [19]. As a kind of earliest inequality, Jensen inequality was widely applied [20].…”

Robust H ∞ state-feedback control for linear systems

“…Therefore, it is another important means of reducing conservatism with respect to the precise estimation. Three main approaches are employed: the free-weighting matrix [18,19], the Jensen inequality [20,21] and the convex optimization method, as well as their combinations [22][23][24][25]. However, in recent developments some terms have been neglected due to the derivative of the LKF being estimated, which may lead to conservative conditions.…”