在具有时间变化的参数的单一扰动延迟系统中,能否实现指数稳定? 一个全面的分析分析
Ran Chen1, Min Ouyang2, Jinju Zhang3
1School of Electronic Science and Engineering, Hunan University of Information Technology, Changsha, 410151, China.
Heliyon
|March 22, 2024
概括
本研究分析了复杂系统中的指数稳定性,这些复杂系统具有延迟和不断变化的参数. 它引入了一种使用线性矩阵不等式 (LMI) 的新方法,绕过常见假设,为动态系统提供更强大的稳定性分析.
科学领域:
- 控制理论 控制理论
- 系统工程 系统工程
- 应用数学 应用数学 应用数学
背景情况:
- 奇点扰乱系统在多个时间尺度上模拟复杂的动态.
- 这些系统的微小延迟带来了重大的分析挑战.
- 现有的方法通常依赖于关于子系统稳定的潜在限制性假设.
研究的目的:
- 在具有时间变化的参数的奇异扰动延迟系统中研究指数稳定性.
- 开发一种新的稳定性分析方法,不假设快速子系统的指数稳定性.
- 通过数值模拟和比较研究来验证拟议的方法.
主要方法:
- 单一扰动理论的应用.
- 使用线性矩阵不等式 (LMIs) 开发稳定性分析框架.
- 在稳定性分析中包括时间变化的参数.
主要成果:
- 介绍了一种基于LMI的新方法,用于分析复杂系统中的指数稳定性.
- 该方法有效地处理有延迟和时间变化的参数的系统,而没有对快速子系统稳定性的预先假设.
- 数字模拟证实了拟议方法的稳定性和有效性,与现有技术相比,显示了较好的稳定性性能.
结论:
- 这项研究提供了一个更全面的理解指数稳定在单一扰动延迟系统.
- 开发的基于LMI的方法为分析具有时间变化的参数的复杂动态系统提供了有价值的工具.
- 这些发现在工程和数学建模中具有潜在的应用,这些系统普遍存在.
相关概念视频
01:28Stability
115
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...
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...
115
01:21Linear Approximation in Time Domain
81
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,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
81
01:18Second Order systems II
108
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
108
01:24BIBO stability of continuous and discrete -time systems
392
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....
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....
392
01:24Pole and System Stability
291
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...
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...
291
01:24Transient and Steady-state Response
176
In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state...
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state...
176