Lecture

Observability and Controllability

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In course

EE-611: Linear system theory

The course covers control theory and design for linear time-invariant systems : (i) Mathematical descriptions of systems (ii) Multivariables realizations; (iii) Stability ; (iv) Controllability and Observability; (v) Minimal realizations and coprime fracti ...

Description

This lecture covers the concepts of observability and controllability in linear systems. It starts by defining the necessary and sufficient conditions for a system to be observable and controllable. The lecture then delves into the reachability of states and pseudo-state trajectories. It discusses the implications of coprimeness and the realization of systems from a state-space perspective. The importance of having no input decoupling for observability is highlighted.

Instructor

Philippe Müllhaupt

Expertise Nonlinear Control (Geometry and Algebra)Classical DynamicsRoboticsStatistics Mission Provide rigorous technical and scientific training in nonlinear control, classical mechanics, and statistical theory Current Work Research and teaching in the fields of control theory, statistics, dynamical systems, and general mechanics. Philippe Mullhaupt received his Diplôme d Education Ingï¿½nieur | Electricitï¿½ 1993 – 1993 EPFL DEA | Automatique et Traitement du Signal 199

Official source

Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Information engineering

Control theory and engineering: Control theory

Related concepts (31)

State-space representation

In control engineering, model based fault detection and system identification a state-space representation is a mathematical model of a physical system specified as a set of input, output and variables related by first-order (not involving second derivatives) differential equations or difference equations. Such variables, called state variables, evolve over time in a way that depends on the values they have at any given instant and on the externally imposed values of input variables.

Roll-on/roll-off

Roll-on/roll-off (RORO or ro-ro) ships are cargo ships designed to carry wheeled cargo, such as cars, motorcycles, trucks, semi-trailer trucks, buses, trailers, and railroad cars, that are driven on and off the ship on their own wheels or using a platform vehicle, such as a self-propelled modular transporter. This is in contrast to lift-on/lift-off (LoLo) vessels, which use a crane to load and unload cargo. RORO vessels have either built-in or shore-based ramps or ferry slips that allow the cargo to be efficiently rolled on and off the vessel when in port.

Lecture

A lecture (from lēctūra ) is an oral presentation intended to present information or teach people about a particular subject, for example by a university or college teacher. Lectures are used to convey critical information, history, background, theories, and equations. A politician's speech, a minister's sermon, or even a business person's sales presentation may be similar in form to a lecture. Usually the lecturer will stand at the front of the room and recite information relevant to the lecture's content.

Hubble Space Telescope

The Hubble Space Telescope (often referred to as HST or Hubble) is a space telescope that was launched into low Earth orbit in 1990 and remains in operation. It was not the first space telescope, but it is one of the largest and most versatile, renowned both as a vital research tool and as a public relations boon for astronomy. The Hubble telescope is named after astronomer Edwin Hubble and is one of NASA's Great Observatories.

Controllability

Controllability is an important property of a control system and plays a crucial role in many control problems, such as stabilization of unstable systems by feedback, or optimal control. Controllability and observability are dual aspects of the same problem. Roughly, the concept of controllability denotes the ability to move a system around in its entire configuration space using only certain admissible manipulations. The exact definition varies slightly within the framework or the type of models applied.

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Lecture

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Controllability