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Ee263_course_reader - Lecture Notes for EE263 Stephen Boyd Introduction to Linear Dynamical Systems Autumn 2010-11 Copyright Stephen Boyd Limited

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Unformatted text preview: Lecture Notes for EE263 Stephen Boyd Introduction to Linear Dynamical Systems Autumn 2010-11 Copyright Stephen Boyd. Limited copying or use for educational purposes is fine, but please acknowledge source, e.g., “taken from Lecture Notes for EE263, Stephen Boyd, Stanford 2010. ” Contents Lecture 1 – Overview Lecture 2 – Linear functions and examples Lecture 3 – Linear algebra review Lecture 4 – Orthonormal sets of vectors and QR factorization Lecture 5 – Least-squares Lecture 6 – Least-squares applications Lecture 7 – Regularized least-squares and Gauss-Newton method Lecture 8 – Least-norm solutions of underdetermined equations Lecture 9 – Autonomous linear dynamical systems Lecture 10 – Solution via Laplace transform and matrix exponential Lecture 11 – Eigenvectors and diagonalization Lecture 12 – Jordan canonical form Lecture 13 – Linear dynamical systems with inputs and outputs Lecture 14 – Example: Aircraft dynamics Lecture 15 – Symmetric matrices, quadratic forms, matrix norm, and SVD Lecture 16 – SVD applications Lecture 17 – Example: Quantum mechanics Lecture 18 – Controllability and state transfer Lecture 19 – Observability and state estimation Lecture 20 – Some final comments Basic notation Matrix primer Crimes against matrices Least-squares and least-norm solutions using Matlab Solving general linear equations using Matlab Low rank approximation and extremal gain problems Exercises EE263 Autumn 2010-11 Stephen Boyd Lecture 1 Overview • course mechanics • outline & topics • what is a linear dynamical system? • why study linear systems? • some examples 1–1 Course mechanics • all class info, lectures, homeworks, announcements on class web page: www.stanford.edu/class/ee263 course requirements: • weekly homework • takehome midterm exam (date TBD) • takehome final exam (date TBD) Overview 1–2 Prerequisites • exposure to linear algebra ( e.g. , Math 103) • exposure to Laplace transform, differential equations not needed , but might increase appreciation: • control systems • circuits & systems • dynamics Overview 1–3 Major topics & outline • linear algebra & applications • autonomous linear dynamical systems • linear dynamical systems with inputs & outputs • basic quadratic control & estimation Overview 1–4 Linear dynamical system continuous-time linear dynamical system (CT LDS) has the form dx dt = A ( t ) x ( t ) + B ( t ) u ( t ) , y ( t ) = C ( t ) x ( t ) + D ( t ) u ( t ) where: • t ∈ R denotes time • x ( t ) ∈ R n is the state (vector) • u ( t ) ∈ R m is the input or control • y ( t ) ∈ R p is the output Overview 1–5 • A ( t ) ∈ R n × n is the dynamics matrix • B ( t ) ∈ R n × m is the input matrix • C ( t ) ∈ R p × n is the output or sensor matrix • D ( t ) ∈ R p × m is the feedthrough matrix for lighter appearance, equations are often written ˙ x = Ax + Bu, y = Cx + Du • CT LDS is a first order vector differential equation...
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This note was uploaded on 12/04/2011 for the course EE 263 at Stanford.

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Ee263_course_reader - Lecture Notes for EE263 Stephen Boyd Introduction to Linear Dynamical Systems Autumn 2010-11 Copyright Stephen Boyd Limited

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