Fixed-Time Stability of Nonlinear Impulsive Systems and its Application to Inertial Neural Networks
This article is concerned with the fixed-time stability (FTS) problem of nonlinear impulsive systems (NISs). By means of the impulsive control mechanism and Lyapunov functions theory, several sufficient conditions are established to ensure the FTS of general NISs. Meanwhile, some novel impulse-depen...
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| description | This article is concerned with the fixed-time stability (FTS) problem of nonlinear impulsive systems (NISs). By means of the impulsive control mechanism and Lyapunov functions theory, several sufficient conditions are established to ensure the FTS of general NISs. Meanwhile, some novel impulse-dependent settling-time estimation schemes are developed, which fully considers the influence of stabilizing impulses and destabilizing impulses on the convergence rate of the system states. The proposed schemes establish a quantitative relationship between the upper bound of the settling time and impulse effects. It shows that stabilizing impulses can accelerate the convergence rate of the system states and leads to the upper bound of the settling time being smaller. Conversely, destabilizing impulses can reduce it and make the upper bound of the settling time larger. Then, the theoretical results are applied to delayed inertial neural networks (DINNs), where two kinds of controllers are designed to realize fixed-time synchronization of the considered systems in the impulse sense. Finally, some numerical examples are provided to illustrate the validity of the proposed theoretical results. |
| doi_str_mv | 10.1109/TNNLS.2022.3185664 |
| format | Article |
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By means of the impulsive control mechanism and Lyapunov functions theory, several sufficient conditions are established to ensure the FTS of general NISs. Meanwhile, some novel impulse-dependent settling-time estimation schemes are developed, which fully considers the influence of stabilizing impulses and destabilizing impulses on the convergence rate of the system states. The proposed schemes establish a quantitative relationship between the upper bound of the settling time and impulse effects. It shows that stabilizing impulses can accelerate the convergence rate of the system states and leads to the upper bound of the settling time being smaller. Conversely, destabilizing impulses can reduce it and make the upper bound of the settling time larger. Then, the theoretical results are applied to delayed inertial neural networks (DINNs), where two kinds of controllers are designed to realize fixed-time synchronization of the considered systems in the impulse sense. 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Finally, some numerical examples are provided to illustrate the validity of the proposed theoretical results.</description><subject>Artificial neural networks</subject><subject>Asymptotic stability</subject><subject>Convergence</subject><subject>Delayed inertial neural networks (DINNs)</subject><subject>Delays</subject><subject>fixed-time stability (FTS)</subject><subject>Impulses</subject><subject>impulsive control mechanism</subject><subject>Liapunov functions</subject><subject>Lyapunov theorems</subject><subject>Neural networks</subject><subject>nonlinear impulsive systems (NISs)</subject><subject>Nonlinear systems</subject><subject>Settling</subject><subject>Stability</subject><subject>Stability criteria</subject><subject>Synchronization</subject><subject>Time dependence</subject><subject>Time synchronization</subject><subject>Upper bound</subject><subject>Upper bounds</subject><issn>2162-237X</issn><issn>2162-2388</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkU1r3DAQhkVpacI2f6CFIuilF2_1YX0dQ2jShWV7yBZ6E7I9BqW25Upy2v33UbLbPXQu78A88zLMi9B7StaUEvNlv9tt79eMMLbmVAsp61foklHJKsa1fn3u1c8LdJXSAykliZC1eYsuuFCKKmUuUXvr_0JX7f0I-D67xg8-H3Do8S5Mg5_ARbwZ52VI_rEAh5RhTNhNHfY54et5Hnzrsg8TzgFvJojZuwHvYIkvkv-E-Cu9Q296NyS4OukK_bj9ur_5Vm2_321urrdVywXNVQ2yVh0nhtUCQBGoOyVrIV0vSqs7bXRTRqqRuu15T6Vu-p42olMNkdQ0fIU-H33nGH4vkLIdfWphGNwEYUmWSc2U5kzygn76D30IS5zKdZYZxikVtMgKsSPVxpBShN7O0Y8uHiwl9jkF-5KCfU7BnlIoSx9P1kszQnde-ffzAnw4Ah4AzmOji58R_AkCkotW</recordid><startdate>20240201</startdate><enddate>20240201</enddate><creator>Hua, Lanfeng</creator><creator>Zhu, Hong</creator><creator>Zhong, Shouming</creator><creator>Zhang, Yuping</creator><creator>Shi, Kaibo</creator><creator>Kwon, Oh-Min</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| subjects | Artificial neural networks Asymptotic stability Convergence Delayed inertial neural networks (DINNs) Delays fixed-time stability (FTS) Impulses impulsive control mechanism Liapunov functions Lyapunov theorems Neural networks nonlinear impulsive systems (NISs) Nonlinear systems Settling Stability Stability criteria Synchronization Time dependence Time synchronization Upper bound Upper bounds |
| title | Fixed-Time Stability of Nonlinear Impulsive Systems and its Application to Inertial Neural Networks |
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