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A state space approach to the analysis of zeros of MIMO LTI discrete-time systems is presented. The basic mathematical tools used in this analysis are the Moore-Penrose pseudoinverse and singular value decomposition of the first nonzero Markov parameter of a system. The book starts with definition of invariant zeros and goes as far as a general characterization of output-zeroing inputs and the corresponding solutions, explicit formulas for maximal output-nulling invariant subspaces and for the zero dynamics. The objective of this book is to render the reader familiar with a certain method of analysis of multivariable zeros (which goes beyond the classical approach) and related problems. The minimal mathematical background that is required from the reader is a working knowledge of linear algebra and difference equations. The reader should be familiar with the basic concepts of linear system theory.

Control theory. --- Discrete-time systems. --- Digital control systems. --- Théorie de la commande --- Systèmes échantillonnés --- Commande numérique --- Engineering. --- Systems theory. --- Control Engineering. --- Systems Theory, Control. --- Discrete-time systems --- Control theory --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Construction --- System theory. --- Control engineering. --- Robotics. --- Mechatronics. --- Control, Robotics, Mechatronics. --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Machine theory --- Control engineering --- Control equipment --- Engineering instruments --- Programmable controllers

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This book develops a general analysis and synthesis framework for impulsive and hybrid dynamical systems. Such a framework is imperative for modern complex engineering systems that involve interacting continuous-time and discrete-time dynamics with multiple modes of operation that place stringent demands on controller design and require implementation of increasing complexity--whether advanced high-performance tactical fighter aircraft and space vehicles, variable-cycle gas turbine engines, or air and ground transportation systems. Impulsive and Hybrid Dynamical Systems goes beyond similar treatments by developing invariant set stability theorems, partial stability, Lagrange stability, boundedness, ultimate boundedness, dissipativity theory, vector dissipativity theory, energy-based hybrid control, optimal control, disturbance rejection control, and robust control for nonlinear impulsive and hybrid dynamical systems. A major contribution to mathematical system theory and control system theory, this book is written from a system-theoretic point of view with the highest standards of exposition and rigor. It is intended for graduate students, researchers, and practitioners of engineering and applied mathematics as well as computer scientists, physicists, and other scientists who seek a fundamental understanding of the rich dynamical behavior of impulsive and hybrid dynamical systems.

Automatic control. --- Control theory. --- Dynamics. --- Discrete-time systems. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Dynamics --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Digital control systems --- Discrete mathematics --- System analysis --- Linear time invariant systems --- Actuator. --- Adaptive control. --- Algorithm. --- Amplitude. --- Analog computer. --- Arbitrarily large. --- Asymptote. --- Asymptotic analysis. --- Axiom. --- Balance equation. --- Bode plot. --- Boundedness. --- Calculation. --- Center of mass (relativistic). --- Coefficient of restitution. --- Continuous function. --- Convex set. --- Differentiable function. --- Differential equation. --- Dissipation. --- Dissipative system. --- Dynamical system. --- Dynamical systems theory. --- Energy. --- Equations of motion. --- Equilibrium point. --- Escapement. --- Euler–Lagrange equation. --- Exponential stability. --- Forms of energy. --- Hamiltonian mechanics. --- Hamiltonian system. --- Hermitian matrix. --- Hooke's law. --- Hybrid system. --- Identity matrix. --- Inequality (mathematics). --- Infimum and supremum. --- Initial condition. --- Instability. --- Interconnection. --- Invariance theorem. --- Isolated system. --- Iterative method. --- Jacobian matrix and determinant. --- Lagrangian (field theory). --- Lagrangian system. --- Lagrangian. --- Likelihood-ratio test. --- Limit cycle. --- Limit set. --- Linear function. --- Linearization. --- Lipschitz continuity. --- Lyapunov function. --- Lyapunov stability. --- Mass balance. --- Mathematical optimization. --- Melting. --- Mixture. --- Moment of inertia. --- Momentum. --- Monotonic function. --- Negative feedback. --- Nonlinear programming. --- Nonlinear system. --- Nonnegative matrix. --- Optimal control. --- Ordinary differential equation. --- Orthant. --- Parameter. --- Partial differential equation. --- Passive dynamics. --- Poincaré conjecture. --- Potential energy. --- Proof mass. --- Quantity. --- Rate function. --- Requirement. --- Robust control. --- Second law of thermodynamics. --- Semi-infinite. --- Small-gain theorem. --- Special case. --- Spectral radius. --- Stability theory. --- State space. --- Stiffness. --- Supply (economics). --- Telecommunication. --- Theorem. --- Transpose. --- Uncertainty. --- Uniform boundedness. --- Uniqueness. --- Vector field. --- Vibration. --- Zeroth (software). --- Zeroth law of thermodynamics.