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Unformatted text preview: Lecture Notes for EE263 Stephen Boyd Introduction to Linear Dynamical Systems Autumn 201011 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 – Leastsquares Lecture 6 – Leastsquares applications Lecture 7 – Regularized leastsquares and GaussNewton method Lecture 8 – Leastnorm 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 Leastsquares and leastnorm solutions using Matlab Solving general linear equations using Matlab Low rank approximation and extremal gain problems Exercises EE263 Autumn 201011 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 continuoustime 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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