Robust fuzzy delayed sampled-data control for nonlinear active suspension systems with varying vehicle load and frequency-domain constraint

This article studies the Takagi-Sugeno (T-S) fuzzy delayed sampled-data $$\mathcal {H}_\infty $$ H ∞ control problem for a class of intelligent suspension systems with varying vehicle load and frequency-domain constraint. The T-S fuzzy model is utilized to characterize the varying vehicle load. Considering the transmission delay, a robust fuzzy delayed sampled-data control mechanism is newly propounded for suspension systems. According to the Lyapunov stability theory, a useful theorem is proposed based on the Wirtinger inequality to guarantee the states of the active suspension system being asymptotically stabilized with the required $$\mathcal {H}_\infty $$ H ∞ performance by the proposed controller. Moreover, the suspension constrained requirements are also satisfied within the finite frequency domain. Finally, simulation examples are presented to attest to the usefulness and superiority of the proposed controller.

Distributed Event-Triggered Output Synchronization of Complex-Valued Memristive Reaction-Diffusion Complex Networks with Spatial Sampled-Data

This study addresses the problem of output quasisynchronization for coupled complex-valued memristive reaction-diffusion complex networks via the distributed event-triggered control scheme. First, by using the separate method, set value mapping, and intermediate value theorem, the complex-valued memristive reaction-diffusion complex networks can be transferred into two semi-uncertain real-valued reaction-diffusion complex networks. Second, a distributed output piecewise event-triggered control (OPETC) scheme with spatial sampled-data is first proposed including a spatial sampling event-triggered generator and spatiotemporal sampling state feedback controller. Furthermore, this scheme can effectively save the measurement resources and lower the update rate of controllers in spatial and time domain. Third, the synchronization analysis is considered by utilizing an appropriate Lyapunov function, the Halanay inequality, and the improved Wirtinger inequality. Subsequently, several output event-triggered quasisynchronization criteria are derived. The relations among event trigger conditions, spatial sampling interval, convergence rate, and control gain are given by rigorous mathematical derivation. Finally, multiple simulations are compared to substantiate the validation of the OPETC scheme.

Quantitative Stability in the Geometry of Semi-discrete Optimal Transport

We show quantitative stability results for the geometric “cells” arising in semi-discrete optimal transport problems. We first show stability of the associated Laguerre cells in measure, without any connectedness or regularity assumptions on the source measure. Next we show quantitative invertibility of the map taking dual variables to the measures of Laguerre cells, under a Poincarè-Wirtinger inequality. Combined with a regularity assumption equivalent to the Ma–Trudinger–Wang conditions of regularity in Monge-Ampère, this invertibility leads to stability of Laguerre cells in Hausdorff measure and also stability in the uniform norm of the dual potential functions, all stability results come with explicit quantitative bounds. Our methods utilize a combination of graph theory, convex geometry, and Monge-Ampère regularity theory.

A Hybrid Event Trigger Mechanism and Time-Delay Partitioning Are Applied to Event-Driven Control Systems

This paper proposes an idea of using time-delay partitioning to construct a Lyapunov–Krasovskii functional (LKF) to analyse event-driven network control systems (NCSs) with the H∞ performance. Firstly, select a mixed event-driven mechanism, in which an adjustable absolute trigger mechanism is added to the trigger condition. Trigger term can be indicated to use a delay model. Secondly, a suitable LKF is created, which makes use of time-delay partitioning. Based on Wirtinger inequality and linear matrix inequalities (LMI), the close system with H∞ performance index level is global uniform ultimate bounded. Finally, a numerical simulation example proves the effectiveness of the proposed method.

Simultaneous approximation of Birkhoff interpolation and the associated sharp inequalities

This paper gives a kind of sharp simultaneous approximation error estimation of Birkhoff interpolation [Formula: see text], [Formula: see text] where [Formula: see text] and [Formula: see text] is the Birkhoff interpolation based on [Formula: see text] pairs of numbers [Formula: see text] with its P[Formula: see text]lya interpolation matrix to be regular. First, based on the integral remainder formula of Birkhoff interpolation, we refer the computation of [Formula: see text] to the norm of an integral operator. Second, we refer the values of [Formula: see text] and [Formula: see text] to two explicit integral expressions and the value of [Formula: see text] to the computation of the maximum eigenvalue of a Hilbert–Schmidt operator. At the same time, we give the corresponding sharp Wirtinger inequality [Formula: see text] and sharp Picone inequality [Formula: see text].

Robust H∞ filtering for Markovian jumping static neural networks with time-varying delays

The problem of robust H∞ filtering for Markovian jumping static neural networks with time-varying delays is considered in this paper. The effect of the activation function on the time delays is comprehensively considered. Based on Wirtinger inequality, a new inequality is quoted to solve the Lyapunov functions with the double-integral terms. Then, a less conservative result on the robust H∞ filtering is obtained, which guarantees the resulting error systems stochastically stable and satisfies a prescribed H∞ performance index. The effectiveness of the developed results is finally demonstrated by numerical examples.