Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Networked Control Systems: Fundamentals and Stability Analysis

In course

ME-427: Networked control systems

This course offers an introduction to control systems using communication networks for interfacing sensors, actuators, controllers, and processes. Challenges due to network non-idealities and opportunities offered by communication will be analyzed. ...

Description

This lecture introduces the organization of the course and reviews linear system theory. It covers topics such as the challenges and opportunities in Networked Control Systems, software installation for exercises, dynamical systems, linear time-varying systems, invariant and time-invariant systems, equilibrium states, stability analysis, and the stability test through eigenvalues. The instructor emphasizes the importance of understanding equilibria and stability properties in control systems.

Instructor

Giancarlo Ferrari Trecate

Official source

Related concepts (31)

Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.

Control theory

Control theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required.

Dynamical systems theory

Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle.

Linear time-invariant system

In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance; these terms are briefly defined below. These properties apply (exactly or approximately) to many important physical systems, in which case the response y(t) of the system to an arbitrary input x(t) can be found directly using convolution: y(t) = (x ∗ h)(t) where h(t) is called the system's impulse response and ∗ represents convolution (not to be confused with multiplication).

Linear system

In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications. For example, the propagation medium for wireless communication systems can often be modeled by linear systems.

Related lectures (57)

Stability and Reachability in Multivariable Control

Explores stability, reachability, and controllability in linear systems, emphasizing their significance in system analysis.

SISO Polynomial Controllers: Sylvester Matrix, Internal Model Principle

Covers the design of SISO polynomial controllers using concepts such as the Sylvester matrix and model matching.

Multivariable Control: System Theory and Applications

Covers system theory, classic feedback control, and applications in green building and natural gas refrigeration plants.

Discrete-time Systems and Lyapunov Theory

Covers the review of linear discrete-time systems and Lyapunov theory, focusing on stability and equilibria.

Convolution and Laplace Transform