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This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations.In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every n-th orde

Boundary value problems. --- Nonselfadjoint operators. --- Eigenvalues. --- Differential equations.

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This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems. The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications. The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications. This book has been adopted as a textbook at the following universities: ? University of Stuttgart, Germany Royal Institute of Technology, Sweden Johannes Kepler University, Austria Georgia Tech, USA University of Washington, USA Ohio University, USA

Mathematics --- Network analysis (Planning) --- Multiagent systems --- Graphic methods. --- Mathematical models. --- Addition. --- Adjacency matrix. --- Algebraic graph theory. --- Algorithm. --- Automorphism. --- Bipartite graph. --- Cardinality. --- Cartesian product. --- Circulant graph. --- Combinatorics. --- Complete graph. --- Computation. --- Connectivity (graph theory). --- Controllability. --- Convex combination. --- Corollary. --- Cycle graph (algebra). --- Cycle space. --- Degree (graph theory). --- Degree matrix. --- Diagonal matrix. --- Diameter. --- Differentiable function. --- Dimension. --- Directed graph. --- Division by zero. --- Dynamical system. --- Eigenvalues and eigenvectors. --- Equilibrium point. --- Estimation. --- Estimator. --- Existential quantification. --- Extremal graph theory. --- Graph (discrete mathematics). --- Graph theory. --- Identity matrix. --- Incidence matrix. --- Information exchange. --- Initial condition. --- Interconnection. --- Iteration. --- Kalman filter. --- Kronecker product. --- LTI system theory. --- LaSalle's invariance principle. --- Laplacian matrix. --- Least squares. --- Line graph. --- Linear map. --- Lipschitz continuity. --- Lyapunov function. --- Lyapunov stability. --- Markov chain. --- Mathematical optimization. --- Matrix exponential. --- Measurement. --- Multi-agent system. --- Nash equilibrium. --- Natural number. --- Network topology. --- Nonnegative matrix. --- Notation. --- Observability. --- Optimal control. --- Optimization problem. --- Pairwise. --- Parameter. --- Path graph. --- Permutation matrix. --- Permutation. --- Positive semidefinite. --- Positive-definite matrix. --- Probability. --- Quantity. --- Random graph. --- Random variable. --- Rate of convergence. --- Requirement. --- Result. --- Robotics. --- Scientific notation. --- Sensor. --- Sign (mathematics). --- Simplicial complex. --- Special case. --- Spectral graph theory. --- Stochastic matrix. --- Strongly connected component. --- Subset. --- Summation. --- Supergraph. --- Symmetric matrix. --- Systems theory. --- Theorem. --- Theory. --- Unit interval. --- Upper and lower bounds. --- Variable (mathematics). --- Vector space. --- Without loss of generality.