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

Finite-Time Stability for Interval Type-2 Fuzzy Nonlinear Systems via an Observer-Based Sliding Mode Control

This paper concentrates on the problem of asynchronous ℋ∞$$ {\mathscr{H}}_{\infty } $$ filtering for singular Markov jump systems under DoS attacks, in which the unknown probability information cases are considered. To better describe cyber security problem, DoS attacks are considered as encountered randomly and modeled by a set of stochastic variables obeying Bernoulli distribution. Besides, hidden Markov model with partially known probability information is proposed to handle the cases that the Markov state information of the system is restrictedly accessed, and the transition probability information and observation probability information can not be directly obtained. A set of criteria are derived to analyze the regularity, causality, and stochastic stability for the filtering error system with an ℋ∞$$ {\mathscr{H}}_{\infty } $$ performance index. Furthermore, an asynchronous filter design method is proposed to against DoS attacks. Finally, a numerical example and a practical example modeled by a DC motor are given to demonstrate the effectiveness of the proposed method.

ℋ∞ filtering for discrete‐time hidden singular Markov jump systems subject to partially known probability information under DoS attacks

In this paper, we expect to design a multi-objective robust filter for fuzzy singularly perturbed systems (SPSs) with Markov switching By utilizing the Takagi and Sugeno (T-S) fuzzy model and the Markov jump model, both the nonlinearity and the sudden changes in the parameters or structures are considered in the description of SPSs Based on some acquired conditions, the final filtering error system can be assured stochastically stable with a prescribed dissipative performance index Finally, the filter gains can be gained by solving these conditions

Multi-objective robust filtering for fuzzy singularly perturbed systems with Markov-switching

This paper investigates the H∞ filtering problem for a class of discrete-time singular Markov jump nonlinear systems against hybrid attacks via a fuzzy-model-based method, in which the hybrid attacks contain deception attacks and denial of service attacks. Two random variables subject to the Bernoulli distribution are used to describe whether the hybrid attacks are encountered during the measurement output of the original system being transmitted to the filter. By using linear matrix inequality technology and Lyapunov stability theory, some sufficient conditions are given to guarantee the considered systems are stochastically admissible and meet H∞ performance index γ. The design approach of the secure filter and a specific form to acquire the expected secure filter gains are obtained, respectively. Finally, to demonstrate the effectiveness of the proposed approach, both a numerical example and a practical example are provided. 

Fuzzy-model-based ℋ∞ filtering for discrete-time singular Markov jump nonlinear systems against hybrid attacks

This paper focuses on the fuzzy control problem for a class of semi-Markov jump singularly perturbed nonlinear systems with actuator saturation. Nonlinearities in the underlying systems are tackled with the Takagi-Sugeno fuzzy model. As distinct from the previous achievements, the case that the semi- Markov kernel with partially known information is taken into account such that the underlying systems can be extended to a wider scope. Given that actuator saturation is ubiquitous in engineering systems, the convex hull method is embraced to address this circumstance. To reduce the conservativeness of the obtained results, on the basis of Lyapunov stability theory and LaSalle's invariance principle, some criteria related to the sojourn time are presented. Next, the mean-square exponential stability of the underlying system is obtained based on the derived results. Finally, further experiment to verify the feasibility of the proposed methodology is given by a tunnel diode circuit model. 

Hao Shen

Papers

Finite-Time Stability for Interval Type-2 Fuzzy Nonlinear Systems via an Observer-Based Sliding Mode Control

ℋ∞ filtering for discrete‐time hidden singular Markov jump systems subject to partially known probability information under DoS attacks

Multi-objective robust filtering for fuzzy singularly perturbed systems with Markov-switching

Fuzzy-model-based ℋ∞ filtering for discrete-time singular Markov jump nonlinear systems against hybrid attacks

Fuzzy $\mathcal{H}_\infty$ Control of Semi-Markov Jump Singularly Perturbed Nonlinear Systems with Partial Information and Actuator Saturation