Journal
NEURAL COMPUTING & APPLICATIONS
Volume 34, Issue 16, Pages 13649-13666Publisher
SPRINGER LONDON LTD
DOI: 10.1007/s00521-022-07177-6
Keywords
Stochastically asymptotic stability; Linear convex combination (LCC) approach; Reciprocally convex inequality (RCI); Linear matrix inequalities (LMIs)
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Funding
- National Natural Science Foundation of China [62173081]
- Research Foundation of Department of Education of Liaoning Province [LJKZ0476]
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This paper discusses the stochastic stability of genetic regulatory networks (GRNs) with semi-Markov switching and time-varying delays. By introducing Legendre polynomials and weighted Legendre polynomials, integral inequalities are derived and Lyapunov-Krasovskii functionals are established. Sufficient conditions for stochastically asymptotic stability are proposed using free-weight matrices and the acquired integral inequalities.
This paper discusses the stochastic stability for genetic regulatory networks (GRNs) with semi-Markov switching and time-varying delays where the transition rates (TRs) of the modes are partially unknown. By proposing vectors with three Legendre polynomials and three weighted Legendre polynomials, two free-matrix-based integral inequalities are derived, which involves several existing ones as their special cases. Then, two appropriate Lyapunov-Krasovskii functionals (LKFs) are established to be apt for the acquired inequalities. By introducing some free-weight matrices and utilizing the acquired integral inequalities, new sufficient conditions are proposed to ensure the stochastically asymptotic stability of analyzed networks in the mean-square sense. Finally, two simulation examples are put forward to show the effectiveness and less conservatism of the presented criteria.
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