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FURTHER ON PETROVIĆ'S TYPES INEQUALITIES
IQBAL, WASIM,REHMAN, ATIQ UR,FARID, GHULAM,RATHOUR, LAXMI,SHARMA, M.K.,MISHRA, VISHNU NARAYAN The Korean Society for Computational and Applied M 2022 Journal of applied mathematics & informatics Vol.40 No.5-6
In this article, authors derived Petrović's type inequalities for a class of functions, namely, called exponentially h-convex functions. Also, the associated results for coordinates has been derived by defining exponentially h-convex functions on coordinates.
Exponential H∞ Control for Singular Systems with Time-varying Delay
Jiemei Zhao,Zhonghui Hu 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.4
This paper studies the exponential admissibility and H∞ control problems for a class of singular systemswith time-varying delay in state. Firstly, an exponential admissibility criterion is obtained based on linear matrixinequalities (LMIs). It is worth mentioning that the derivative of the time-varying delay does not need to be smallerthan one. Based on the proposed condition, a new delay-dependent H∞ controller is also given, which guaranteesthe admissibility and the H∞ performance g . Numerical examples are given to illustrate the effectiveness of theproposed method.
Zhaoxia Duan,Imran Ghous,Yuanqing Xia,Jahanzeb Akhtar 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.8
This paper deals with the problem of exponential stability and H∞ control of two-dimensional (2-D) switched discrete systems with mixed time-varying delays. Firstly, this work suggests some improvements to Lyapunov-Krasovskii functional (LKF) discussed in the previous literature. Such improvements have been achieved by introducing some new terms containing the summations of state vector in single and double forms in an effort to capture the extra information related to time delays. Secondly, delay-dependent conditions based on the improved LKF are derived for the exponential stability and H∞ performance of 2-D switched systems in the form of linear matrix inequalities (LMIs) by virtue of the average dwell time approach. Thirdly, a state-feedback controller is designed to ensure the exponential stability of the overall closed-loop system under consideration with a desirable H∞ disturbance attenuation level γ. Finally, a suitable example is provided which highlights the benefits of the proposed results by comparing them with the results available in literature both in terms of conservativeness and computational burden.
Linlin Hou,Pengfei Ma,Xuan Ma,Haibin Sun 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.4
The problem of H∞ exponential synchronization for switched cellular neural networks that are subjected to multiple exogenous disturbances is investigated. The exogenous disturbances are rejected and attenuated by combining disturbance observer-based control with H∞ control. Based on the admissible edge-dependent average dwell time scheme and the Lyapunov-Krasovskii functional technique, a synchronization criterion formulated by linear matrix inequalities is procured for switched cellular neural networks with external disturbances. Finally, the effectiveness of the obtained results is verified through a numerical simulation.
An Ji Ho,Kim Han Sol 대한전기학회 2024 Journal of Electrical Engineering & Technology Vol.19 No.5
This paper proposes a novel approach to designing a fault-tolerant H∞ sampled-data fuzzy fi lter using exponential time-varying gains. The utilization of exponential time-varying gains not only achieves a reduction in convergence time but also provides relaxation in the numerical optimization of design conditions. Also, through the use of a robust control technique, the designed fi lter is equipped with enhanced fault-tolerant capabilities. In addition, suffi cient conditions for ensuring H∞ -based state estimation performance are derived as linear matrix inequalities (LMIs) based on the Lyapunov–Krasovskii functional (LKF). Finally, simulation results demonstrate the superior performance of the proposed method when compared to existing methodologies.
Delay-Dependent H_∞ Control for Jumping Delayed Systems with Two Markov Processes
Hao Shen,Yuming Chu,Shengyuan Xu,Zhengqiang Zhang 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.3
This paper addresses the H_∞ control problem for jumping delayed systems with two separable Markov processes. The objective is to design a controller such that the resulting closed-loop system is exponentially mean-square stable with a given decay rate and satisfies a prescribed H_∞ performance level. A decay-rate-dependent condition is obtained for the existence of admissible controllers in term of linear matrix inequalities. Two numerical examples are presented to demonstrate the effectiveness of the proposed method.
Sampled-data H<sub>~</sub> fuzzy filtering for nonlinear systems with missing measurements
Koo, G.B.,Park, J.B.,Joo, Y.H. North-Holland ; Elsevier Science Ltd 2017 FUZZY SETS AND SYSTEMS Vol.316 No.-
<P>In this paper, a sampled-data H-infinity fuzzy filtering problem is considered for nonlinear systems with missing measurements. The nonlinear sampled-data system and missing measurements are assumed to be represented by a Takagi-Sugeno (T-S) fuzzy system and an independent, identically distributed Bernoulli random process, respectively. Based on the fuzzy system, the H-infinity fuzzy filtering problem is formulated to design the sampled-data fuzzy filter. By using the exponential mean-square stability definition, the stability condition with an H-infinity performance is guaranteed for the fuzzy system with the sampled-data fuzzy filter, and its sufficient condition is converted into the linear matrix inequality (LMI) format. Finally, an example is provided to verify the effectiveness of the proposed fuzzy filtering technique. (C) 2016 Elsevier B. V. All rights reserved.</P>
Maharajan Chinnamuniyandi,Raja Ramachandran,Jinde Cao,Grienggrai Rajchakit,Xiaodi Li 제어·로봇·시스템학회 2018 International Journal of Control, Automation, and Vol.16 No.2
This paper mainly focuses on a novel H∞ control design to handle the global robust exponential stability problem for uncertain stochastic neutral-type neural networks (USNNNs) with mixed time-varying delays. Here the delays are assumed to be both discrete and distributed, which means that the lower and upper bounds can be derived. Firstly, we draw a control law for stabilized and stability of the neutral-type neural networks (NNNs). Secondly, by employing the Lyapunov-Krasovskii functional(LKF) theory, Jensen’s integral inequality, new required sufficient conditions for the global robust exponential stability of the given neural networks (NNs) are established in terms of delay-dependent linear matrix inequalities (LMIs), which can be easily checked in practice. The conditions obtained are expressed in terms of LMIs whose feasibility can be verified easily by MATLAB LMI control toolbox. Moreover, we have compared our work with previous one in the existing literature and showed that it reduces conservatism. Finally, one numerical example with their simulations is given to validate the effectiveness of our proposed theoretical results.
Various shadowing properties for time varying maps
Javad Nazarian Sarkooh 대한수학회 2022 대한수학회보 Vol.59 No.2
This paper is concerned with the study of various notions of shadowing of dynamical systems induced by a sequence of maps, so-called time varying maps, on a metric space. We define and study the shadowing, h-shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties of these dynamical systems. We show that h-shadowing, limit shadowing and s-limit shadowing properties are conjugacy invariant. Also, we investigate the relationships between these notions of shadowing for time varying maps and examine the role that expansivity plays in shadowing properties of such dynamical systems. Specially, we prove some results linking s-limit shadowing property to limit shadowing property, and h-shadowing property to s-limit shadowing and limit shadowing properties. Moreover, under the assumption of expansivity, we show that the shadowing property implies the h-shadowing, s-limit shadowing and limit shadowing properties. Finally, it is proved that the uniformly contracting and uniformly expanding time varying maps exhibit the shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties.
Saima Rashid,Muhammad Aslam Noor,Khalida Inayat Noor 강원경기수학회 2019 한국수학논문집 Vol.27 No.4
In the article, we present several new Hermite-Hadamard and Hermite-Hadamard-Fej\'{e}r type inequalities for the exponentially $(\hbar,\mathfrak{m})$-convex functions via an extended generalized Mittag-Leffler function. As applications, some variants for certain typ e of fractional integral operators are established and some remarkable special cases of our results are also have been obtained.