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BIBO stability of continuous and discrete -time systems

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.

Stability

Stability

The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...

Pole and System Stability

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.

Stability of Equilibrium Configuration

Stability of Equilibrium Configuration

Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...

Stability of structures

Stability of structures

In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...

Stability of Equilibrium Configuration: Problem Solving

Stability of Equilibrium Configuration: Problem Solving

The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...

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Updated: May 27, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Stability of Boolean and continuous dynamics.

Fakhteh Ghanbarnejad¹, Konstantin Klemm

¹Bioinformatics Group, Institute for Computer Science, University of Leipzig, Härtelstraße 16-18, D-04107 Leipzig, Germany. fakhteh@bioinf.uni-leipzig.de

Physical Review Letters

|November 24, 2011

Summary

This summary is machine-generated.

Boolean dynamics stability differs from continuous models. Random networks with high sensitivity show stable continuous dynamics, challenging prior classifications.

Related Experiment Videos

Last Updated: May 27, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Area of Science:

Systems biology
Computational biology
Theoretical biology

Background:

Biological regulation is often modeled using continuous rate equations for chemical concentrations.
Discretization of these systems leads to Boolean dynamics, where stability is defined by resistance to 'damage spreading' from perturbations.

Purpose of the Study:

To investigate the discrepancy between stability classifications in continuous and Boolean models of biological regulatory networks.
To determine how network properties influence stability under different modeling approaches.

Main Methods:

Comparison of stability properties between continuous differential equation models and their discretized Boolean counterparts.
Analysis of random network models with varying node sensitivity to perturbations.

Main Results:

The study reveals significant differences in stability classifications between continuous and Boolean dynamics.
Random networks characterized by high node sensitivity exhibit stable dynamics in the continuous model, contrary to Boolean stability predictions.
Boolean dynamics stability criteria do not accurately reflect the behavior of underlying continuous systems under small perturbations.

Conclusions:

The stability of biological regulatory networks is highly dependent on the modeling approach (continuous vs. Boolean).
Boolean dynamics may not reliably predict the stability of real biological systems, especially those with sensitive components.
Further research is needed to reconcile these different modeling frameworks for accurate biological system analysis.