| Citation: |
Minghui Jiang, Xue Fang, Junhao Hu. FINITE-TIME STABILITY OF NONAUTONOMOUS AND AUTONOMOUS LINEAR SYSTEMS[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1720-1738. doi: 10.11948/20210397
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FINITE-TIME STABILITY OF NONAUTONOMOUS AND AUTONOMOUS LINEAR SYSTEMS
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Abstract
In this research, in view of Lyapunov theory, the finite time stability (FTS) conditions of linear time-delay systems are investigated. Firstly, by using matrix inequality and algebraic inequality methods, the conditions for FTS of nonautonomous and autonomous systems are given respectively. Compared with the existing literature, the judging conditions are easier to verify and have a better conservative type. In addition, by employing the provided FTS theoretical results, several novel criteria for ensuring the stabilization of autonomous delay systems and the stability of impulsive switched nonautonomous time-varying systems are obtained. Eventually, several concrete examples are put forward to validate the theoretical findings.
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Keywords:
- Finite time stability /
- time delay /
- Lyapunov functional /
- impulsive switching
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References
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Minghui Jiang, Xue Fang, Junhao Hu. FINITE-TIME STABILITY OF NONAUTONOMOUS AND AUTONOMOUS LINEAR SYSTEMS[J]. Journal of Applied Analysis & Computation, 2023, 13(4): 1720-1738. doi: 10.11948/20210397
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Figure 1.
The dynamical behaviors of
$ \mu(t) $ -
Figure 2.
The dynamical behaviors of
$ \mu^T(t)W\mu(t) $ $ \beta_1=1, \beta_2=44.7230, W=I, \mathcal{T}=6.3 $ -
Figure 3.
The trajectories of
$ \mu_{1}(t), \mu_{2}(t) $ $ \mu_1(0)=0.7070, \mu_2(0)=-0.707. $ -
Figure 4.
The trajectories of
$ \mu^T(t)W\mu(t) $ $ t. $ -
Figure 5.
The dynamical behaviors of
$ \mu(t) $ $ \mu_1(0)=0.4, \mu_2(0)=0.2, \mu_3(0)=0.4 $ -
Figure 6.
The dynamical behaviors of
$ \mu^T(t)W\mu(t) $ $ \beta_1=0.36, \beta_2= 3, W=I, \mathcal{T}=7 $ -
Figure 7.
The dynamical behaviors of
$ \mu(t) $ -
Figure 8.
The dynamical behaviors of
$ \mu^T(t)W\mu(t) $ $ \beta_1=0.36, \beta_2= 3, W=I, \mathcal{T}=7 $ -
Figure 9.
The dynamical behaviors of
$ \mu^T(t)W\mu(t) $ -
Figure 10.
The dynamical behaviors of
$ \mu^T(t)W\mu(t) $