Università Roma Tre

Linear Systems
1. INTRODUCTION TO LINEAR SYSTEMS
1.1. Modelling
1.2. State-Space Representation
2. NONLINEAR SYSTEMS AND LINEARIZATION
2.1. Motivations and Definitions
2.2. Linearization Method
3. DIFFERENTIAL EQUATIONS
3.1. Linear Differential Equations with Constant Coefficients
3.2. Exponential Matrix
3.3. Free Evolution
3.4. Forced Evolution
4. RELATIONSHIP BETWEEN REPRESENTATIONS
4.1. From State-Spate to Transfer Function
4.2. From Transfer Function to State-Spate
5. MODAL DECOMPOSITION
5.1. Eigenvalues and Eigenvectors
5.2. Coordinate Transformation
5.3. Diagonalization and Jordanization
6. STRUCTURAL PROPERTIES
6.1. Controllability and Observability
6.2. Controllability and Observability Kalman Forms
6.3. Kalman Canonical Decomposition
7. REALIZATION AND CANONICAL FORMS
7.1. Realization
7.2. Canonical Forms for Realization

1. An Introduction to Linear Control Systems, Thomas E. Fortmann, Konrad L. Hitz
2. Lecture Notes (http://gasparri.dia.uniroma3.it/Stuff/complementi_teoria_dei_sistemi.pdf)

Linear Systems
1. EIGENVALUE ASSIGNMENT PROBLEM
1.1. Eigenvalue assignment using state feedback
1.1.1. Assignment Theorem (SISO/MIMO)
1.1.2. Assignment Unicity Theorem (SISO)
1.2. Stabilization Problem
1.3. State Asymptotic Observer
1.4. Separation Principle
1.5. Eigenvalue placement using output feedback
2. LINEAR OUTPUT REGULATION PROBLEM
2.1. Full-Information Problem
2.2. Error-Feedback Problem
3. ROOT LOCUS
2.8. Exact Root Locus Analysis
2.9. Approximate Root Locus Analysis
2.10. Root Locus Design

Nonlinear Systems
1. INTRODUCTION TO NONLINEAR SYSTEMS
1.1. Fundamental Properties
1.2. Lipschitz Condition
1.3. Existence and Unicity of Solution
1.4. Comparison Lemma
2. LYAPUNOV STABILITY
2.1. Autonomous Systems
2.2. Stability Definition
2.3. Stability Theorem (Direct Criterion)
2.4. Chetaev Instability Theorem
2.5. Lyapunov Control Functions (Krasovskii)
2.6. Invariance Principle (LaSalla Theorem)
2.7. Stability Theorem for Linear Systems (Indirect Criterion)

Main Textbook:
1. Sistemi di controllo (Vol. 2), Alberto Isidori
2. Lecture Notes (http://gasparri.dia.uniroma3.it/Stuff/complementi_teoria_dei_sistemi.pdf)


Main Textbook:
1. Nonlinear Systems (3rd Edition), Hassan K. Khalil