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ABSTRACT In this article, new linear matrix inequality (LMI) conditions are proposed to guarantee robust stability of the closed‐loop of the linear time‐invariant one‐dimensional uncertain system by dealing with both continuous‐time (CT) and discrete‐time (DT) cases. These improved conditions for robust state feedback control combine the non‐monotonic approach and Finsler's technique. The benefit of the non‐monotonic approach returns to the utility of an arbitrary number of quadratic functions by considering the higher order derivatives of the vector field in the CT case (or the higher order differences of the vector field in the DT case). Finsler's technique aims to solve the closed‐loop stability problem in a larger parametric space. The strong points of the suggested LMI conditions are easy to program, eliminate the product between the state matrix and Lyapunov matrices, reduce the constraints by avoiding the decrease monotonically along trajectories for each quadratic Lyapunov function, guarantee the robust stability of the closed‐loop by using a state‐feedback gain. The simulation results show and confirm the effectiveness of these proposed conditions. [ABSTRACT FROM AUTHOR]

The aim of this study is to address the challenge of H∞ filtering for 2-D systems with time delays. We will employ the well-known Fornasini-Marchesini state model with delay to mathematically describe these 2-D systems. Our objective is to develop a full-order filter that not only ensures the asymptotic stability of the expanded system but also maintains H∞ performance. Our approach will rely on Linear Matrix Inequalities (LMIs) to establish the conditions for the filter’s existence and convert the filter design problem into a convex optimization problem. Finally, we conclude with an illustrative example to demonstrate the effectiveness of the proposed filter design.

In this article, we propose the issue of H∞ deconvolution filtering for two‐dimensional (2D) systems described by the Fornasini–Marchesini local state‐space model. The main challenge is the design of a deconvolution filter to rebuild the 2D signal so that the filter error system is asymptotically stable and preserves a guaranteed H∞ performance. To overcome this issue, we use some free matrix variables to eliminate coupling between Lyapunov matrix and system matrices to obtain sufficient conditions in linear matrix inequality form to ensure the desired stability and performance of the error systems in the first time. Moreover, we use the orthogonal moments to extract the feature vectors to generate the input system, with the minimum information with and without noise. Simulation examples are provided to show that the new design technology proposed in this article achieves better H∞ performance than the existing design methods. Finally, this work can be very helpful tools for the practitioners in telecommunication, and data scientists to aid them in deconvolution, diagnostic, and transmission. [ABSTRACT FROM AUTHOR]

Summary: This article deals with the problems of stability and stabilization for a class of discrete‐time switched systems with time‐varying delay under arbitrary switching signal. First, sufficient conditions guaranteeing the asymptotic stability of the unforced system are developed, by using the switched Lyapunov‐Krasovskii functional method. Then, based on the obtained results, a state feedback controller is designed in order to ensure the asymptotic stability of the closed‐loop system. Furthermore, slack variables are introduced for more relaxation. The proposed approach is proved to have some less conservative results than some existing works. Finally, numerical examples are provided to illustrate the effectiveness and the merit of the proposed method and to compare the obtained results with some previous works in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to address the problem of assessing the stability of singular time-varying delay systems. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, a model transformation using a three-terms approximation of the delayed state is exploited. Based on the lifting method and the Lyapunov–Krasovskii functional (LKF) method, a new linear matrix inequality (LMI) is obtained, allowing conclusions on stability to be drawn using the scaled small gain theorem (SSG). The use of SSG theorem for stability of singular systems with time-varying delay has not been investigated elsewhere in the literature. This represents the main novelty of this article. The result is applicable for assessing the stability of both singular systems and neutral systems with time-varying delays. The less conservativeness of the stability test is illustrated by comparison with recent literature results. [ABSTRACT FROM AUTHOR]