Università Roma Tre

Linear Systems
1. INTRODUCTION TO LINEAR SYSTEMS
1.1. Modelling
1.2. State-Space Representation
2. DIFFERENTIAL EQUATIONS
2.1. Linear Differential Equations with Constant Coefficients
2.2. Exponential Matrix
2.3. Free Evolution
2.4. Forced Evolution
3. RELATIONSHIP BETWEEN REPRESENTATIONS
3.1. From State-Spate to Transfer Function
3.2. From Transfer Function to State-Spate
4. MODAL DECOMPOSITION
4.1. Eigenvalues and Eigenvectors
4.2. Coordinate Transformation
4.3. Diagonalization and Jordanization
5. STRUCTURAL PROPERTIES
5.1. Controllability and Observability
5.2. Controllability and Observability Kalman Forms
5.3. Kalman Canonical Decomposition
7. EIGENVALUE ASSIGNMENT PROBLEM
7.1. Eigenvalue assignment using state feedback
7.1.1. Assignment Theorem (SISO/MIMO)
7.1.2. Assignment Unicity Theorem (SISO)
7.2. Stabilization Problem
7.3. State Asymptotic Observer
7.4. Separation Principle
7.5. Eigenvalue placement using output feedback
8. LINEAR OUTPUT REGULATION PROBLEM
8.1. Full-Information Problem
8.2. Error-Feedback Problem
Nonlinear Systems
9. INTRODUCTION TO NONLINEAR SYSTEMS
9.1. Fundamental Properties
9.2. Lipschitz Condition
9.3. Existence and Unicity of Solution
9.4. Comparison Lemma
10. LYAPUNOV STABILITY
10.1. Autonomous Systems
10.2. Stability Definition
10.3. Stability Theorem (Direct Criterion)
10.4. Chetaev Instability Theorem
10.5. Lyapunov Control Functions (Krasovskii)
10.6. Invariance Principle (LaSalla Theorem)
10.7. Stability Theorem for Linear Systems (Indirect Criterion)

Linear Systems
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)
3. Sistemi di controllo (Vol. 2), Alberto Isidori

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