BIBO stability

Summary

In signal processing, specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take inputs. If a system is BIBO stable, then the output will be bounded for every input to the system that is bounded. A signal is bounded if there is a finite value B > 0 such that the signal magnitude never exceeds B, that is :For discrete-time signals: \exists B \forall n(\ |y[n]| \leq B) \quad n \in \mathbb{Z} :For continuous-time signals: \exists B \forall t(\ |y(t)| \leq B) \quad t \in \mathbb{R} Time-domain condition for linear time-invariant systems Continuous-time necessary and sufficient condition For a continuous time linear time-invariant (LTI) system, the condition for BIBO stability is that the impulse response, h(t) , be absolutely integrable, i.e., its L1 norm exists. : \int_{-\infty}^\infty \left|h(t)\right|,\mathord{\operat

Official source

https://en.wikipedia.org/wiki/BIBO_stability

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (5)

Related publications

Related people (3)

Related people

Related units (1)

Related units

Related concepts (17)

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 a

In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker at Siemens

Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to feed back into itself. The noti

Related concepts

Related courses (17)

Related courses

Related lectures (33)

Related lectures

Related publications (5)

Frequency Domain Controller Design by Linear Programming Guaranteeing Quadratic Stability

Alireza Karimi, Marc Kunze, Roland Longchamp

In a recent work, a frequency method based on linear programming is proposed to design fixed-order linearly parameterized controllers for stable linear multi- model SISO systems. The method is based on the shaping of the open-loop transfer functions in the Nyquist diagram under a set of linear constraints guaranteeing a lower bound on the crossover frequency and a linear stability margin. In this paper, this method is extended to guarantee quadratic stability. For this purpose, new linear constraints based on the phase difference of the characteristic polynomials of the models are added in the Nyquist diagram. A simulation example illustrates the effectiveness of the proposed approach.

IEEE2008

Robust PID Controller Design by Linear Programming

Alireza Karimi, Marc Kunze, Roland Longchamp

A linear programming approach is proposed to tune fixed-order linearly parameterized controllers for stable LTI plants. The method is based on the shaping of the open-loop transfer function in the Nyquist diagram. A lower bound on the crossover frequency and a new linear stability margin which guarantees lower bounds for the classical robustness margins are defined. Two optimization problems are proposed and solved by linear programming. In the first one the robustness margin is maximized for a given lower bound on the crossover frequency, whereas in the second one the integrated error is minimized with constraints on the new stability margin. The method can directly consider multi-model as well as frequency-domain uncertainties. An application to a high-precision double-axis positioning system illustrates the effectiveness of the proposed approach.

2006

Robust Controller Design by Linear Programming with Application to a Double-Axis Positioning System

Alireza Karimi, Marc Kunze, Roland Longchamp

2007