Titlebook: Linear Systems; Gordon Blower Textbook 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Sw

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Linear Systems and Their Description, notion of input, state and output, and the fundamental operations that relate these. There is a pictorial representation in terms of block diagrams. The chapter gives block diagrams for ODE, and shows how to express higher order scalar ODE in terms of first order matrix ODE. Examples include feedback systems and the damped harmonic oscillator.

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Solving Linear Systems by Matrix Theory,s .. The fundamental example of a linear system (., ., ., .) in continuous time . is introduced via a differential equation and solved using the matrix exponential applied to .. Simple examples motivate the definitions.

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Eigenvalues and Block Decompositions of Matrices,m for . has implications for the transfer function of (., ., ., .). There are refinements for specific classes of ., such as positive definite matrices. The chapter also covers controllable and observable systems.

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Transfer Functions, Frequency Response, Realization and Stability,e transfer function gives rise to gain and phase, which have intuitive interpretations in signal processing, and which are well illustrated in Nyquist plots. The chapter characterizes bounded-input bounded-output stability in terms of the poles of the transfer function.

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Algebraic Characterizations of Stability, for polynomials is applied in simple cases, and there is a detailed discussion of Youla’s parametrization of the stabilizing controllers for a rational SISO system. The results are expressed in terms of principal ideal domains using undergraduate algebra. There are explicit links to the Laplace transform results of previous chapters.

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Stability and Transfer Functions via Linear Algebra,erion. There are several results showing how algebraic operations on rational transfer functions can be realized by operations on MIMO systems (., ., ., .), which can be helpful for computation. The discrete Fourier transform is expressed in matricial style.

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Design of DMD Projection Lens for Structured Light 3D Measurement,ent technology has a wide range of applications. The image quality of the projection lens determines whether the projection grating can be clearly projected on the detection object in the 3D measurement, which directly affects the detection effect. In this paper, a DMD projection imaging lens suitab

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Handhabung,Ver?ndern oder vorübergehende Aufrechterhalten einer vorgegebenen, r?umlichen Anordnung von bestimmten K?rpern in einem Bezugskoordinatensystem, wobei weitere Bedingungen vorgegeben sein k?nnen, wie z. B. Zeit, Menge und Bewegungsbahn. Im Rahmen der planerischen Betrachtung der Materialflusstechnik

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0302-9743 2006) in Enschede, The Netherlands. EuroSSC 2006 was the ?rst conference of a series aiming at bringing together designers, engineers and researchers to explore two complementary viewpoints: – A device-centric,technology-drivenview: concerning intelligent sensors,s- sor networks and information pro