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See detailRobust Exponential Stability criteria of Uncertain Stochastic Systems with Time-varying Delays
Li, Yumei UL; Guan, Xinping; Luo, Xiaoyuan

in International Journal of Systems Science (2011), 42(4), 601-608

This paper investigates the problem of delay-dependent exponential stability in mean square for continuous-time linear stochastic systems with structured uncertainties and time-varying delays. By applying ... [more ▼]

This paper investigates the problem of delay-dependent exponential stability in mean square for continuous-time linear stochastic systems with structured uncertainties and time-varying delays. By applying descriptor model transformation of the systems, a new type of Lyapunov-Krasovskii functional is constructed, and by introducing some free weighting matrices, some new delay-dependent and delay-independent stability criteria are respectively derived in terms of LMI algorithm. the new stability criteria are less conservative than existing results. Numerical examples demonstrate the new criteria are effective and are an improvement over existing results. [less ▲]

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See detailMultistability of genetic regulatory networks
Pan, Wei UL; Zhang, Z.; Liu, H.

in International Journal of Systems Science (2010), 41(1), 107-118

Multistability is found to be an important recurring theme in synthesis biology. In this article, the multistability analysis problem is investigated by applying control theory and mathematical tools ... [more ▼]

Multistability is found to be an important recurring theme in synthesis biology. In this article, the multistability analysis problem is investigated by applying control theory and mathematical tools. Both the modelling and analysis issues are discussed. Specifically, the genetic regulatory networks (GRNs) with multistability are modelled as switched systems with interval time-varying delays and parameter uncertainties, where the piecewise-affine models are used to approximate the inherent non-linearities existing in the GRNs. Then, by using a novel Lyapunov functional approach and linear matrix inequality (LMI) techniques, a few delay-dependent criteria for the multistability of such genetic regulatory networks are established in the form of LMIs, which can be readily verified by using standard numerical software. A three-component network and a genetic toggle switch with bistability are employed to illustrate the applicability and usefulness of the developed theoretical results. [less ▲]

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