Provide to the students methodologies and techniques for the analysis and modeling of linear time-invariant systems by focusing on the state-space representation. Provide the knowledge for the design of feedback control systems. Derive the state-space model of Multi-Input Multi-Output systems. Provide the knowledge of the structural properties of MIMO dynamical models and the asymptotic observer for the eigenvalue assignment problem and the regulation problem. Provide the students with basic concepts for the analysis of nonlinear system.
Curriculum
teacher profile teaching materials
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)
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
Programme
Linear Systems1. 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)
Core Documentation
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
Type of delivery of the course
Lectures and classroom exercises are planned.Type of evaluation
Learning verification tests are based on two examinations: a written exam of a duration of two hours and an oral exam. The written exam is composed of several exercises aiming at assessing the students capability to apply the fundamental concepts. The oral exam aims at assessing the level of understanding of the fundamental concepts. In order to take the oral exam it is mandatory to have successfully pass the written exam during the current academic year. ----- During the COVID-19 emergency learning verification tests will be conducted according to the art.1 of the Rectoral decree n°. 703 of 5 May 2020 teacher profile teaching materials
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)
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
Programme
Linear Systems1. 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)
Core Documentation
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
Type of delivery of the course
Lectures and classroom exercises are planned.Type of evaluation
Learning verification tests are based on two examinations: a written exam of a duration of two hours and an oral exam. The written exam is composed of several exercises aiming at assessing the students capability to apply the fundamental concepts. The oral exam aims at assessing the level of understanding of the fundamental concepts. In order to take the oral exam it is mandatory to have successfully pass the written exam during the current academic year. ----- During the COVID-19 emergency learning verification tests will be conducted according to the art.1 of the Rectoral decree n°. 703 of 5 May 2020