Robust stability analysis method of time-varying delay uncertain linear system
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A linear system and analysis method technology, applied in the field of time-delay systems, can solve problems such as cumbersome analysis process
Inactive Publication Date: 2018-01-05
HENAN POLYTECHNIC UNIV
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However, when analyzing the robust stability of uncertain systems with interval-varying delays in related technologies, the analysis methods used
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Embodiment 1
[0174] The following three numerical examples are used to verify the simulation to illustrate the effectiveness of the method in this embodiment. Example 1. Consider the following system:
[0175]
[0176] Table 1 gives the lower bound h at different time delays 1 , The upper bound of the maximum time delay allowed for system stability h 2 Value. Compared with the literature [6,8,12,16,23,24,25,26,29,31], the method of this embodiment is less conservative. In addition, compared with other documents, this embodiment involves fewer variables and simple calculations.
[0177]
[0178] Table 1
Embodiment 2
[0179] Example 2. Consider the following system:
[0180]
[0181] For different time delay lower bound h 1 , The upper bound of time delay h to ensure system stability 2 The value is shown in Table 2. It can be seen from Table 2 that compared with the literature [6,7,18,19,20,24,25,26], the method in this example is less conservative.
[0182]
[0183] Table 2
Embodiment 3
[0184] Embodiment 3. Consider the following uncertain system, the system parameters are as follows:
[0185]
[0186] Where: γ 1 ,γ 2 ,γ 3 And γ 4 Are uncertain parameters and satisfy |γ 1 |≤1.6,|γ 2 |≤0.05,|γ 3 |≤0.1,|γ 4 |≤0.3.
[0187] Table 3 gives the lower bound h at different time delays 1 , The upper bound of the maximum time delay allowed for system stability h 2 Value. It can be seen from Table 3 that the robust stability theorem proposed in this embodiment is relatively conservative.
[0188]
[0189] table 3
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Abstract
The invention provides a robust stability analysis method for an uncertain linear system with interval-varying time-delay, comprising: obtaining the nominal system of the uncertain linear system with interval-varying time-delay; constructing a Lyapunov-Krasovskii functional, and The functional determines whether the nominal system is stable, wherein the constructed Lyapunov-Krasovskii functional includes multiple integrals, and the derivative of the Lyapunov-Krasovskii functional is determined based on the Wirtinger type single and double integral inequalities and the convex combination method; in the nominal When the system is stable, the robust stability of the uncertain linear system with interval-varying time-delay is determined. Through the technical scheme of the invention, based on the constructed multiple-integral Lypunov–Krasovskii functional analysis, the robust stability of an uncertain linear system with interval-varying time-delay can be obtained, and less conservative results can be obtained.
Description
Technical field [0001] The invention relates to the technical field of time-delay systems, and in particular to a robust stability analysis method of an interval-variable time-delay uncertain linear system. Background technique [0002] Time lag often appears in various practical systems, such as chemical systems, biological systems, neural network systems, and network control systems. Its existence often leads to poor or unstable performance of related systems. In the past few decades, The research on time-delay systems has attracted close attention. The main purpose of time-delay system stability analysis is to obtain less conservativeness, and the maximum allowable time delay is recognized as the most important indicator. However, when analyzing the robust stability of uncertain systems with interval time-varying delays in related technologies, the analysis methods used are more conservative, and the analysis methods used often introduce too many decision variables, and the e...
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