New Weighted Integral Inequalities and Its Application to Exponential Stability Analysis of Time-Delay Systems

Improved Delay-Dependent Stability Analysis of Fixed-Point State-Space Digital Filters With Time-Varying Delay and Generalized Overflow Arithmetic

“…In fact, the holding of ( 7), ( 9), (12), and ( 13) is based on the special feature of nonlinear function caused by overflow correction mechanism. The usage of those information is an important difference in comparison to the linear discrete-time delayed systems [42], [54]- [56] or traditional Lur'e nonlinear discrete-time delayed systems [61], [62], and it is also the one of important treatments for reducing the conservatism.…”

“…From the research on digital filters point of view, there are only a few works on digital filters considering the time-varying delay [3], [47], [49], [50], and the techniques used therein are all conservative in comparison to the ones developed for the time-delay systems. Recently, many more effective methods have been developed for dealing with time-varying delays, such as augmented Lyapunov functionals [51]- [53], new inequalities [42], [54]- [56], extended reciprocally convex matrix inequalities [57]- [59], etc. From the viewpoint of techniques dealing with the discrete-time delay systems, every term in the Lyapunov functionals is usually required to positive in order to guarantee the positive-definiteness of the functionals.…”

“…(1) Due to the adding of Z 5 and Z 6 respectively defined in (42) and ( 43) into the ∆V (k), several cross terms are introduced to give the relationship between the delayed states, x(k −τ (k)) and x(k −1), and the nonlinear function, f (y(k)), which are not used in the literature [3], [47], [49], [50] and provide extra freedom for finding the solutions of conditions in Theorem 1 so as to reduce the conservatism. (2) The summation term defined by J 1 , J 2 , and J 3 are bounded by using the Wirtinger-based summation inequality, while the similar terms are estimated based on a more conservative inequality, i.e., the Jensen-based summation inequality, in the previous literature [3], [47], [49], [50].…”

Adaptive Memoryless Sliding Mode Control of Uncertain Rössler Systems with Unknown Time Delays

“…In view of this, in [17,18], an in-depth and multivariate study of exponential stability analysis of time-delay systems is carried out. More recently, in [19], the authors derived sufficient conditions for exponentially stable behavior of time-delay systems based on Wirtinger's boundary-integral inequalities. In [20], the authors studied robust exponential stability and its necessary conditions for a class of uncertain linear systems with a single constant delay and uncertain time-invariant parameters.…”

Robust stabilization of T-S fuzzy systems via improved integral inequality

“…To be more specific, an integral inequality proposed in [31] results in the reduction of the conservatism based on the treatment in Fourier theory, particularly in the view of well known Wirtinger inequalities. In [32], the authors developed new integral inequalities by means of the proposed integral inequality in [33] in order to investigate the problem of exponential stability performance of the delayed systems. In [34], the stability criterion for delayed system is studied with the aid of bounding inequalities and augmented LKF.…”