LINEAR SYSTEM THEORY

ING-INF/04 - 9 CFU - 2° Semester

Teaching Staff

MAIDE ANGELA RITA BUCOLO


Learning Objectives

The course aims to drive the students in the acquisition of the basic knowledge and methodology in modeling analysis and control of Linear Time Invariant (LTI) systems in the state space.



Detailed Course Content

1. LTI System Internal Representation: Definition of a Dynamical System - Systems Classification - Linear Time Invariant (LTI) Systems in continuous and discrete time – State space representation - State equation solution by Lagrange - State transition matrix - Equivalent systems and similarity transformations – System modes in continuous and discrete time. Multi-input/Multi-output systems.

2. LTI Input/Output System Representation: Mathematical note on the Laplace and Zeta operator – Relations between the S plane and Z plane (Tustin transformation) - Transfer function - Systems connection and block diagrams – System realizations and minimality - Jordan canonical form.

3. Stability for LTI Systems: Definition of Stability - Internal stability and eigenvalues - Input/output stability and poles (BIBO stability) – Asymptotic stability criteria (Routh and Hurwitz) – Stability in connected systems – Stability and relation between the S plane and Z plane.

4. Input/Output Response in Time Domain : Pulse and step response for first order and second order systems – Step response and pole placement - Step response and zero.

5. Input/Output Response in Frequency Domain: Harmonic function - Frequency response for LTI System - Bode diagrams – Characteristics of the frequency response for first and second order systems – Minimum phase systems.

6. Structural Properties for LTI Systems: Controllability - State feedback controller design for eigenvalues placement - Control canonical form - System decomposition based on the controllability – Observability - Asymptotic observer design (the state estimator) - Control canonical form - System decomposition based on the observability - Principle of separation of estimation and control - Kalman decomposition and transfer function.



Textbook Information

T1) G. F. Franklin et al, Feedback control of dynamic systems, Addison Wesley

T2) R.C.Dorf and R.H. Bishop, Modern Control Systems, Addison Wesley




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