Introduction to Dynamic Systems

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ESE 210
Introduction to Dynamic Systems

Catalog Description: This first course in systems modeling focuses on linear discrete-time systems. We draw on a set of examples used throughout the course as the necessary mathematical tools are developed. The examples demonstrate the breadth of systems models and are drawn from engineering, the biological sciences, and economics. MATLAB will be used extensively. Pre-requisite: MATH 240.
Motivation (2 weeks)
Systems Modeling
Closed
Equations that describe system are known
Open
Simulation needed for system modeling
Complex
Agent based modeling
Review some simple models that are familiar
Geometric Growth model
Loan Repayment/Home mortgage
National Income Model
Exponential Growth/decay
Cohort Population Model
Introduction to use of MATLAB
Modeling change with difference equations
Life cycle of the modeling process
Linear Difference Equations (3 weeks)
Mathematical Properties
Definitions
Existence and uniqueness
Initial conditions
Existence and Uniqueness Theorem
First-order linear equations
General Solution
Amortization example
Cobweb Model
MATLAB
Linear Difference Equations
Homogeneous Equation
Fundamental Set of Solutions
Linear Independence
Solution of Nonhomogeneous Equation
Linear Equations with Constant Coefficients
Characteristic Equation
Systems of First-order Equations
Definitions
Example – Leontief Economic Model
Linear Systems
Systems of Equations in Matrix Format (2 weeks)
Linear Algebra
Matrices and vectors
Elementary Operations
Determinants
Inverses
Linear transformations
Eigenvalues/ eigenvectors
Cohort Population Growth Model
MATLAB
Linear State Equations (3 weeks)
Systems of First-order Difference Equations
State space
Conversion to State Form
Block diagrams
Homogeneous discrete time systems
Natchez Social Structure Example
General solution to linear discrete-time systems
Superposition
Time-invariant Systems
National Income Model Revisited
Equilibrium Points and Stability
Cohort Population Growth Model
Natchez Social Structure Example Revisited
Concepts of Control (4 weeks)
Z-transform
Definition
Sequences and convergence
Rational polynomials, poles and zeros
Transform Properties and Transform Pairs
Transform Solution of Difference Equations
Inversion by Partial Fractions
State Space Methods
ESE 210 John Keenan Page 4/7/2016