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Title of Thesis

Linear Dynamical Systems: An Operational Approach

Author(s)

M SAEED AKRAM

Institute/University/Department Details
Abdus Salam School of Mathematical Sciences / GC University, Lahore
Session
2010
Subject
Mathematics
Number of Pages
68
Keywords (Extracted from title, table of contents and abstract of thesis)
Linear, Dynamical, Systems, Operational, Approach, Willems, behavioral theory, calculus

Abstract
In this work, we take a somewhat different look at the Willems behavioral theory of linear systems. The approach is based on a simplified version of the Heaviside-Mikusinski calculus. The notion of transfer function is ”revived” and it plays a central role in the work.

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S. No. Chapter Title of the Chapters Page Size (KB)
1 0 CONTENTS

 

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1

LINEAR SYSTEMS WITH LOCALLY INTEGRABLE TRAJECTORIES

1.1 Locally integrable functions as a module

1.2 AR-models and their behaviors

1.3 Fundamental exact sequence

1.4 Frequency responses

1.5 When have two AR-models the same behavior?

1.6 Distinguished submodules and the relative dimension

1.7 Properties characterizing the behaviors

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3 2 SOME BASICS OF LINEAR SYSTEMS THEORY

2.1 Some preliminaries

2.2 Controllability

2.3 ”MA-representation” theorem

2.4 Decomposition theorem

2.5 Test for controllability

2.6 Controllability indices

2.7 The complexity and the observability indices

2.8 State representations

2.9 I/O linear systems

2.10 Appendix: Controllability `a la Willems

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4 3 BIBLIOGRAPHY

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