Abstract
This paper investigates the problem of finite-time stability (FTS) for a class of delayed genetic regulatory networks with reaction-diffusion terms. In order to fully utilize the system information, a linear parameterization method is proposed. Firstly, by applying the Lagrange’s mean-value theorem, the linear parameterization method is applied to transform the nonlinear system into a linear one with time-varying bounded uncertain terms. Secondly, a new generalized convex combination lemma is proposed to dispose the relationship of bounded uncertainties with respect to their boundaries. Thirdly, sufficient conditions are established to ensure the FTS by resorting to Lyapunov Krasovskii theory, convex combination technique, Jensen’s inequality, linear matrix inequality, etc. Finally, the simulation verifications indicate the validity of the theoretical results.
Highlights
With the deepening research on biological network, neural network, gene network and other excellent achievements have been produced in recent years [1,2,3,4,5,6]
In order to dispose the nonlinearity in DGRNs-RDTs (3), we propose the following linear parameterization method based on the Lagrange’s mean-value theorem (LMVT) By using the LMVT, there exist variable ξ j (t, ε) ≥ 0, between Hj (t − L(t), ε) and H∗j (ε), j ∈ In, such that
Based on the linear parameterization method, a more accurate feasible region of the finite-time stability (FTS) conditions can be obtained by using the above 2n boundary information matrices
Summary
With the deepening research on biological network, neural network, gene network and other excellent achievements have been produced in recent years [1,2,3,4,5,6]. 3, two main results are proposed, i.e., a linear parameterization method and sufficient FTS conditions of DGRNs-RDTs. In Sect. FTS criterion of the new linear model is established under Dirichlet boundary conditions in terms of LMIs. In order to dispose the nonlinearity in DGRNs-RDTs (3), we propose the following linear parameterization method based on the Lagrange’s mean-value theorem (LMVT) By using the LMVT, there exist variable ξ j (t, ε) ≥ 0, between Hj (t − L(t), ε) and H∗j (ε), j ∈ In, such that. In order to increase the utilization of system information, the nonlinear regulation function is transformed into equation (5) based on the linear parameterization method. Based on the linear parameterization method, a more accurate feasible region of the FTS conditions can be obtained by using the above 2n boundary information matrices. Continuous calculation based on the above algorithm, and we can obtain A +
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