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This monograph discusses the issues of stability and the control of impulsive systems on hybrid time domains, with systems presented on discrete-time domains, continuous-time domains, and hybrid-time domains (time scales). Research on impulsive systems has recently attracted increased interest around the globe, and significant progress has been made in the theory and application of these systems. This book introduces recent developments in impulsive systems and fundamentals of various types of differential and difference equations. It also covers studies in stability related to time delays and other various control applications on the different impulsive systems. In addition to the analyses presented on dynamical systems that are with or without delays or impulses, this book concludes with possible future directions pertaining to this research.

Differentiable dynamical systems. --- Systems theory. --- Dynamical Systems and Ergodic Theory. --- Systems Theory, Control. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Dynamics. --- Ergodic theory. --- System theory. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Systems, Theory of --- Systems science --- Science --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Philosophy

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This volume presents infectious diseases modeled mathematically, taking seasonality and changes in population behavior into account, using a switched and hybrid systems framework. The scope of coverage includes background on mathematical epidemiology, including classical formulations and results; a motivation for seasonal effects and changes in population behavior, an investigation into term-time forced epidemic models with switching parameters, and a detailed account of several different control strategies. The main goal is to study these models theoretically and to establish conditions under which eradication or persistence of the disease is guaranteed. In doing so, the long-term behavior of the models is determined through mathematical techniques from switched systems theory. Numerical simulations are also given to augment and illustrate the theoretical results and to help study the efficacy of the control schemes.

Classical mechanics. Field theory --- Statistical physics --- Epidemiology --- Infectious diseases. Communicable diseases --- Applied physical engineering --- Planning (firm) --- Computer science --- chaos --- toegepaste wiskunde --- theoretische fysica --- informatica --- mathematische modellen --- besmettelijke ziekten --- epidemiologie --- ingenieurswetenschappen --- dynamica

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This volume presents infectious diseases modeled mathematically, taking seasonality and changes in population behavior into account, using a switched and hybrid systems framework. The scope of coverage includes background on mathematical epidemiology, including classical formulations and results; a motivation for seasonal effects and changes in population behavior, an investigation into term-time forced epidemic models with switching parameters, and a detailed account of several different control strategies. The main goal is to study these models theoretically and to establish conditions under which eradication or persistence of the disease is guaranteed. In doing so, the long-term behavior of the models is determined through mathematical techniques from switched systems theory. Numerical simulations are also given to augment and illustrate the theoretical results and to help study the efficacy of the control schemes.

Mathematical models. --- Infectious diseases. --- Computational complexity. --- Statistical physics. --- Epidemiology. --- Mathematical Modeling and Industrial Mathematics. --- Infectious Diseases. --- Complexity. --- Applications of Nonlinear Dynamics and Chaos Theory.

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This book is the first to present the application of the hybrid system theory to systems with EPCA (equations with piecewise continuous arguments). The hybrid system paradigm is a valuable modeling tool for describing a wide range of real-world applications. Moreover, although new technology has produced, and continues to produce highly hierarchical sophisticated machinery that cannot be analyzed as a whole system, hybrid system representation can be used to reduce the structural complexity of these systems. That is to say, hybrid systems have become a modeling priority, which in turn has led to the creation of a promising research field with several application areas. As such, the book explores recent developments in the area of deterministic and stochastic hybrid systems using the Lyapunov and Razumikhin–Lyapunov methods to investigate the systems’ properties. It also describes properties such as stability, stabilization, reliable control, H-infinity optimal control, input-to-state stability (ISS)/stabilization, state estimation, and large-scale singularly perturbed systems.

Hybrid systems. --- Dynamic systems, Hybrid --- Hybrid dynamic systems --- System theory --- Systems theory. --- Mathematical physics. --- Statistical physics. --- Control and Systems Theory. --- Systems Theory, Control. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Mathematical Methods in Physics. --- Statistical Physics and Dynamical Systems. --- Mathematical Physics. --- Physics --- Mathematical statistics --- Physical mathematics --- Statistical methods --- Mathematics --- Control engineering. --- System theory. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Systems, Theory of --- Systems science --- Science --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Philosophy

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Bifurcation theory. --- System analysis. --- Network analysis --- Network science --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Differential equations, Nonlinear --- Stability --- Numerical solutions --- Teoria de la bifurcació --- Anàlisi de sistemes --- Cibernètica --- Física matemàtica --- Models matemàtics --- Teoria de sistemes --- Diagrames de flux --- Disseny de sistemes --- Identificació de sistemes --- Enginyeria de sistemes --- Mètodes de l'espai d'estat --- Sistemes borrosos --- Sistemes de temps discret --- Teoria de control --- Xarxes elèctriques --- Optimització matemàtica --- Teories no lineals --- Sistemes dinàmics diferenciables