关于非线性采样数据系统的稳定性及其连续时间限制
Alexis J Vallarella1, Hernan Haimovich1
1Centro Internacional Franco-Argentino de Ciencias de la Información y de Sistemas (CIFASIS), CONICET-UNR, Ocampo y Esmeralda, 2000 Rosario, Argentina.
ISA transactions
|July 12, 2023
概括
本研究分析了具有不同采样时间的非线性采样数据系统. 它展示了如何通过检查相关的连续时间系统来预测系统稳定性,改进了对非线性系统的现有方法.
科学领域:
- 控制理论 控制理论
- 系统工程 系统工程
- 非线性动力学是一种非线性动力学.
背景情况:
- 非线性采样数据系统在稳定性分析中存在挑战,原因是采样不均.
- 现有的方法往往为这些系统提供有限的稳定性保证 (例如实际稳定性).
- 分析精确的离散时间模型可能很复杂.
研究的目的:
- 开发非线性采样数据系统在非统一采样下稳定性分析的新方法.
- 建立离散时间模型稳定性和连续时间系统稳定性之间的关系.
- 为了实现比目前可能更强的稳定性预测 (非对称稳定性).
主要方法:
- 对非线性采样数据系统的稳定性属性的分析.
- 精确的离散时间模型和相关的连续时间系统 (随着最大采样期接近零) 的稳定性之间的关系的推导.
- 推导结果与关于采样数据系统稳定性的现有文献进行比较.
主要成果:
- 在离散时间模型的稳定性和连续时间系统极限之间建立了新的关系.
- 通过分析连续时间系统来推断采样数据系统稳定性的简化方法.
- 与现有文献相比,可以证明非线性系统具有更强的非对称稳定性.
结论:
- 拟议的方法提供了一种更有效的方式来分析非线性采样数据系统的稳定性.
- 这些发现允许在以前只能实现实际稳定性的情况下,改进 (非对称) 稳定性保证.
- 这种方法通过利用相关的连续时间系统的特性来简化稳定性分析.
相关概念视频
01:24BIBO stability of continuous and discrete -time systems
442
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....
442
01:28Stability
158
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...
158
01:26Feedback control systems
349
Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
349
01:11Sampling Continuous Time Signal
281
In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
In the...
281
01:26Linear Approximation in Frequency Domain
114
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
114
01:31Classification of Systems-II
179
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
179