State bounding for time-delay impulsive and switching genetic regulatory networks with exogenous disturbance

Abstract

<p style='text-indent:20px;'>This paper focuses on the state bounding problem for the time-delay impulsive and switching genetic regulatory networks (ISGRNs) with exogenous disturbances. Firstly, a sufficient criterion for the state bounding is obtained such that all the trajectories of ISGRNs under consideration converge exponentially into a sphere on the basis of an average dwell time (ADT) switching. Besides, globally exponential stability conditions for the considered system are further stated when the exogenous disturbance vanishes. As a special case, the equivalent state bounding criteria are established by using the properties of some special matrices when there exist no impulses at the switching instants in ISGRNs. Finally, an illustrating example is given to demonstrate the derived results. Compared with the existing literatures, the considered genetic regulatory networks (GRNs) have more general structure and the approach adopted in the present paper is more simple than Lyapunov-Krasovskii functional (LKF) approach.</p>

State bounding and synthesis of switched genetic regulatory networks with mixed delays and bounded disturbances

“…So although we only consider constant discrete delays and constant distributed delays in this paper, however, the proposed method can be easily extended to the continuous bounded time‐varying case. Therefore, Theorem 1 is more simpler and easily verified than Yan et al, 42 , Corollary 2 and the estimated state bounding of Theorem 1 is less conservative.…”

“…Choosing u 1 = col(0. transcendental equations are needed to be solved according to Yan et al 42 , Corollary 2 By comparison, the proposed approach in the paper has lower computational complexity than Yan et al 42 ; therefore, it's easier to be applied. The above results are obtained in the case of the constant time delays.…”

“…Compared with the results in Yan et al, 42 this condition involves only $$$ 2N $$$ linear matrix inequalities and does not need to solve the additional $$$ 2 Nn $$$ transcendental equations. Therefore, the proposed method in this paper is more simpler and easily solved than one in 42 …”

“…By using the minimum dwell time method, this condition is derived directly on the basis of the system model and is easy to be verified and realized. Compared with the results in Yan et al, 42 this condition involves only 2N linear matrix inequalities and does not need to solve the additional 2Nn transcendental equations. Therefore, the proposed method in this paper is more simpler and easily solved than one in.…”

“…Therefore, the proposed method in this paper is more simpler and easily solved than one in. 42 2. Based on the results of 2, the reachable set of switched GRNs under consideration is proposed, which is bounded by the Cartesian product of two polytopes or ellipsoids.…”