Robust Stability of Markovian Jumping Genetic Regulatory Networks with Mode-Dependent Delays

• Main Authors: Guang He, Jian-An Fang, Xiaotai Wu
• Format: Article
• Language: English
• Published: Hindawi Limited 2012-01-01
• Series: Mathematical Problems in Engineering
• Online Access: http://dx.doi.org/10.1155/2012/504378

The robust stability analysis problem is investigated for a class of Markovian jumping genetic regulatory networks with parameter uncertainties and mode-dependent delays, which varies randomly according to the Markov state and exists in both translation and feedback regulation processes. The purpose of the addressed stability analysis problem is to establish some easily verifiable conditions under which the Markovian jumping genetic regulatory networks with parameter uncertainties and mode-dependent delays is asymptotically stable. By utilizing a new Lyapunov functional and a lemma, we derive delay-dependent sufficient conditions ensuring the robust stability of the gene regulatory networks in the form of linear matrix inequalities. Illustrative examples are exploited to show the effectiveness of the derived linear-matrix-inequalities- (LMIS-) based stability conditions.