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Related Concept Videos

Stability01:28

Stability

129
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...
129
Linear time-invariant Systems01:23

Linear time-invariant Systems

262
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...
262
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

401
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....
401
Pole and System Stability01:24

Pole and System Stability

301
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...
301
Control System Problem01:21

Control System Problem

119
In an open-loop system, such as a basic thermostat, the poles of the transfer function influence the system's response but do not determine its stability. However, when feedback is introduced to form a closed-loop system, such as an advanced thermostat that adjusts heating based on room temperature, stability is governed by the new poles of the closed-loop transfer function.
When forming a closed-loop system, issues can arise if the poles cross into the unstable region, leading to potential...
119
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

83
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
83

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Stability and stabilizability of linear time-invariant interval systems.

Zhuo Wang1, Tiexiao Xu2

  • 1Zhejiang Provincial Key Laboratory of Ultra-Weak Magnetic-Field Space and Applied Technology, Hangzhou Innovation Institute of Beihang University, Hangzhou, 310051, China; School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing, 100191, China.

ISA Transactions
|November 23, 2023
PubMed
Summary

New methods for linear time-invariant (LTI) interval systems enhance stability analysis and control design. These approaches offer less conservative conditions and reduced computational complexity for improved performance.

Keywords:
Feedback stabilization designLTI interval systemsParameter vertex matricesStabilityStabilizability

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Area of Science:

  • Control Theory
  • Systems Engineering
  • Applied Mathematics

Background:

  • Linear time-invariant (LTI) interval systems present challenges in stability analysis and control design.
  • Existing methods like Kharitonov's theorem and Gerschgorin's disc theorem can be conservative.
  • Computational complexity is a significant factor in practical applications of stability analysis and control.

Purpose of the Study:

  • To propose novel approaches for determining the stability and stabilizability of LTI interval systems.
  • To develop state feedback stabilization controllers for LTI interval systems.
  • To provide methods with improved accuracy and reduced computational load compared to existing techniques.

Main Methods:

  • Development of new stability conditions that are less conservative than established theorems.
  • Formulation of sufficient and necessary conditions for stability, stabilizability, and feedback stabilization.
  • Utilizing a special form of parameter vertex matrices to reduce computational complexity.

Main Results:

  • The proposed stability conditions demonstrate reduced conservatism compared to Kharitonov's theorem and Gerschgorin's disc theorem.
  • The developed methods for stability, stabilizability, and feedback stabilization are proven to be sufficient and necessary.
  • The new approaches exhibit lower computational complexity due to the specific parameter vertex matrices.

Conclusions:

  • The novel methods offer significant advantages for stability analysis and control design in LTI interval systems.
  • Reduced conservatism and computational complexity make these approaches more effective and practical.
  • Numerical and practical examples validate the superiority of the proposed techniques.