Fractional Differential Equations

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

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Differential Equations and Dynamical Systems

This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.

The sector bound approach to quantized feedback control | NOVA. The University of Newcastle's Digital Repository

WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.

Advanced Calculus I

Review of fractional PID controller

In this paper, the exponential stabilization of delayed complex-valued neural networks (DCNNs) is addressed via sampled-data control. First, aperiodic sampled-data control aimed at further reducing the frequency of data transmission is adopted, which covers the periodic sampling as a special case. Then, a free-matrix-based time-dependent Lyapunov functional is specially constructed for stability analysis of closed-loop DCNNs, in which two extra free matrices are introduced and the available information of system states at the sampling instants are fully utilized. Accordingly, some less conservative stability conditions are established. By resorting to a matrix transformation, the design scheme for the feedback gains can be obtained. Meanwhile, the qualitative relationship between the decay rate and the upper bound of the variable sampling period is established and the maximum allowable value of the variable sampling period is determined. Finally, an illustrative example is provided to demonstrate the feasibility of the proposed stabilization criteria.

Exponential Stabilization of Delayed Complex-valued Neural Networks with Aperiodic Sampling: A Free-matrix-based Time-dependent Lyapunov Functional Method

This article addresses the distributed containment control problem in a group of agents governed by second-order dynamics with directed network topologies. Considering there are multiple leaders, we study a general second-order containment controller which can realize several different consensus modes by adjusting control gains. A necessary and sufficient condition on the control gains of the general containment controller is provided. Moreover, the delay sensitivity of the closed-loop multiagent system under the general containment controller is studied; the maximal upper bound of the constant delays is obtained. Finally, several numerical examples are used to illustrate the theoretical results. © 2015 Wiley Periodicals, Inc. Complexity 21: 112–120, 2016

Distributed containment control of second‐order multiagent systems with input delays under general protocols

In this article, the problem of sampled-data control is considered for semi-Markovian jump systems (FSMJSs) with actuator saturation by Takagi–Sugeno fuzzy model method. First, mode-dependent Lyapunov functional consisting of the two-sided closed-loop function is constructed. On the basis of this function, stochastically stable criteria are presented in terms of linear matrix inequalities (LMIs). Then, based on the stochastically stable criteria, mode-dependent sampled-data controllers are designed for FSMJSs. As a corollary, stable criteria and controller design are also proposed for the general FSMJSs without actuator saturation. The improved LMI-based optimisation conditions are obtained to estimate the region of attraction. Finally, numerical examples are provided to show the effectiveness and significant improvement of the method presented.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-cta.2020.0147

Sampled-data control for semi-Markovian jump systems with actuator saturation via fuzzy model approach

pth moment $${\cal D}$$-stability/stabilization of linear discrete-time stochastic systems

This paper is concerned with the dissipative filtering problem for a class of stochastic jumping neural networks. The model under consideration is subject to unreliable communication links, which result in some network-induced phenomena such as packet dropouts, sensor nonlinearity and unknown / partly known mode information. A set of Bernoulli distributed white sequences are introduced to govern these phenomena occurring in a random way. The aim is to design a mixed filter, which ensures that the filtering error system is extended stochastically dissipative. Such a mixed filter has the advantages of both the model independent filter and the asynchronous filter. With the help of Lyapunov–Krasovskii methodology and an improved matrix decoupling approach, sufficient conditions for the existence of such a filter are presented by solving some convex optimization problems. A numerical example is given to verify the effectiveness of the proposed method.

Hao Shen

Papers

Exponential Stabilization of Delayed Complex-valued Neural Networks with Aperiodic Sampling: A Free-matrix-based Time-dependent Lyapunov Functional Method

Distributed containment control of second‐order multiagent systems with input delays under general protocols

Sampled-data control for semi-Markovian jump systems with actuator saturation via fuzzy model approach

pth moment $${\cal D}$$-stability/stabilization of linear discrete-time stochastic systems

On dissipative filtering over unreliable communication links for stochastic jumping neural networks based on a unified design method