Related Experiment Video
Updated: Dec 6, 2025
08:35
Interactive and Visualized Online Experimentation System for Engineering Education and Research
Published on: November 24, 2021
2.8K
H∞ control for singular fractional-order interval systems: The 0<α<1 case.
1Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, No.800 Dong Chuan Road, Min Hang, Shanghai 200240, PR China.
ISA Transactions
|October 12, 2020
Summary
This study addresses H∞ control for singular fractional-order interval systems. Novel methods ensure system stability and performance, with controllers designed for state feedback and dynamic output feedback applications.
Area of Science:
- Control Theory
- Systems Engineering
- Fractional Calculus
Background:
- Singular fractional-order systems present unique control challenges.
- Interval uncertainty complicates stability and performance analysis.
- H∞ control is crucial for robust system performance.
Purpose of the Study:
- To investigate H∞ control problems for singular fractional-order interval systems.
- To develop conditions for admissibility and H∞ performance.
- To design state feedback and dynamic output feedback H∞ controllers.
Main Methods:
- Novel conditions for the bounded real lemma (H∞ norm) were established.
- Sufficient conditions for admissibility and H∞ performance were derived.
- State feedback and dynamic output feedback controllers were synthesized.
Main Results:
- New criteria for H∞ bounded real lemma in singular fractional-order systems.
- Derived sufficient conditions for system admissibility and H∞ performance.
- Successfully designed state feedback and dynamic output feedback H∞ controllers.
Conclusions:
- The proposed methods effectively address H∞ control for singular fractional-order interval systems.
- The designed controllers ensure system stability and H∞ performance.
- Illustrative examples validate the practical applicability of the results.
Related Concept Videos
01:22Basic Continuous Time Signals
581
Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...
581
01:27Time and frequency -Domain Interpretation of PI Control
314
Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires...
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires...
314
01:21First Order Systems
284
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
284
01:25The Intermediate Value Theorem
105
The Intermediate Value Theorem is a foundational result in calculus that guarantees the existence of solutions within certain intervals for continuous functions. Formally, the Intermediate Value Theorem states that if a function f is continuous on the closed interval [a, b], and if N is any value between f(a) and f(b), then there exists at least one c ∈ (a, b) such that f(c) = N. This theorem is instrumental in proving the existence of roots and in analyzing the behavior of continuous...
105
01:24Limits at Infinity
82
The function that decreases as the input becomes very large provides a clear example of how mathematical functions can behave at extreme values. When the input increases continuously, the output becomes smaller and smaller, getting closer to a particular fixed value. Although the output never actually reaches this value, it moves nearer to it without limit. This behavior is a fundamental concept in understanding how functions behave as the input grows indefinitely. The graphical representation...
82
01:28Inequalities
103
Inequalities express mathematical relationships where two values are not equal and are compared using symbols such as <, >, ≤, or ≥. These expressions define a range of possible solutions rather than a single value. Interval notation provides a concise way to express these solution sets, especially when the variable spans a continuous range. An open interval, written as (a, b), excludes the endpoints, while a closed interval [a, b] includes them. There are also half-open...
103