PVDnotes

PVDnotes - Numerical Linear Algebra for Signals Systems and Control Paul M Van Dooren University of Louvain B-1348 Louvain-la-Neuve Belgium Draft

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Unformatted text preview: Numerical Linear Algebra for Signals Systems and Control Paul M. Van Dooren University of Louvain, B-1348 Louvain-la-Neuve, Belgium Draft notes prepared for the Graduate School in Systems and Control Spring 2003 ii Contents 1 SCOPE AND INTRODUCTION 1 1.1 Scope of the Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 About Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Numerical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Basic Problems in Numerical Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 IDENTIFICATION 23 2.1 SISO identification from the impulse response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2 State-space realizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3 Balanced realizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.4 Pad´ e algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.5 Multi-input multi-output impulse response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.6 Input-Output Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.7 Recursive least squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.8 MIMO identification via I/O pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.9 Linear prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3 STATE SPACE ANALYSIS 67 3.1 Orthogonal State-Space Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.2 Condensed Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.3 Controllability, Observability and Minimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.4 Staircase form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.5 Subspaces and Minimal Realizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.6 Poles and Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4 STATE SPACE DESIGN 91 4.1 State feedback and pole placement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.2 Multi-input feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.3 Observers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4.4 Lyapunov and Sylvester Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106....
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This note was uploaded on 07/21/2011 for the course MAD 5932 taught by Professor Gallivan during the Spring '06 term at FSU.

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PVDnotes - Numerical Linear Algebra for Signals Systems and Control Paul M Van Dooren University of Louvain B-1348 Louvain-la-Neuve Belgium Draft

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