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Related Concept Videos

Linear time-invariant Systems01:23

Linear time-invariant Systems

978
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
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Stability01:28

Stability

428
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...
428
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
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BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

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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....
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Constraints and Statical Determinacy01:26

Constraints and Statical Determinacy

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In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...
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Classification of Systems-I01:26

Classification of Systems-I

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Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
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Related Experiment Video

Updated: Feb 22, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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A solid criterion based on strict LMI without invoking equality constraint for stabilization of continuous singular

Xuefeng Zhang1, YangQuan Chen2

  • 1School of Sciences, Northeastern University, Shenyang, Liaoning 110004, China.

ISA Transactions
|September 19, 2017
PubMed
Summary

This study presents a new method for stabilizing linear continuous singular systems using linear matrix inequalities (LMIs). The proposed formulation is a necessary and sufficient condition, offering a more reliable and tractable solution than existing approaches.

Keywords:
Generalized quadratic stabilityLinear matrix inequalities(LMIs)Quadratic admissibilitySingular systemsStabilization

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Area of Science:

  • Control Systems Engineering
  • Systems Theory
  • Applied Mathematics

Background:

  • Singular systems present unique challenges in control theory due to their inherent properties.
  • Existing methods for stabilizing singular systems often involve complex equality constraints and can be numerically unstable.
  • The singularity of specific matrix terms (Ω=PET+SQ) poses a significant hurdle in stabilization criteria.

Purpose of the Study:

  • To develop a novel and effective linear matrix inequality (LMI) formulation for the stabilization of linear continuous singular systems.
  • To propose a criterion that avoids the drawbacks associated with equality constraints and singularity issues in existing methods.
  • To provide a directly solvable and numerically reliable approach for singular system stabilization.

Main Methods:

  • Formulation of strict linear matrix inequalities (LMIs) without equality constraints.
  • Development of a necessary and sufficient condition for system stabilization.
  • Utilization of LMI toolbox for direct computation of feasible solutions.

Main Results:

  • A complete and effective LMIs formulation for singular system stabilization.
  • The proposed criterion overcomes the invalidity issues caused by the singularity of Ω=PET+SQ.
  • The method is more tractable and reliable in numerical simulations compared to existing techniques.

Conclusions:

  • The presented LMI formulation offers a robust and efficient solution for stabilizing linear continuous singular systems.
  • The new criterion addresses critical limitations of previous methods, enhancing stability analysis.
  • The approach provides a practical tool for researchers and engineers working with singular systems.