Author Description

This dissertation, "Stability Analysis of Uncertain Genetic Regulatory Newtworks" by Jiewei, Li,, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Genetic regulatory network (GRN) is a fundamental research area in systems biology. This thesis studies the stability of a class of GRN models. First, a condition is proposed to ensure the robust stability of uncertain GRNs with SUM regulatory functions. It is assumed that the uncertainties are in the form of a parameter vector that determines the coefficients of the model via given functions. Then, the global asymptotic stability conditions of uncertain GRNs affected by disturbances and time delays are further explored. The conditions are obtained by solving a convex optimization problem by exploring the sum of squares (SOS) of matrix polynomials and by introducing polynomially parameter-dependent Lyapunov-Krasovskii functionals (LKFs). Moreover, based on the uncertain GRNs with guaranteed disturbance attenuation, it is shown that estimates of the sought stable uncertainty sets can be obtained through a recursive strategy based on parameter-dependent Lyapunov functions and the SOS. Second, the stability conditions of GRNs described by piecewise models are considered. Depending on whether the state partitions and mode transitions are known or unknown as priori, the proposed networks are divided into two categories, i.e., switched GRNs and hybrid GRNs. It is shown that, by using common polynomial Lyapunov functions and piecewise polynomial Lyapunov functions, two conditions are established to ensure the global asymptotic stability for switched and hybrid