Stability analysis of nonlinear time-delayed systems with application to biological models - Kruthika, H.A.; Mahindrakar, Arun D.; Pasumarthy, Ramkrishna (Zielona Góra: Uniwersytet Zielonogórski)
In this paper, we analyse the local stability of a gene-regulatory network and immunotherapy for cancer modelled as nonlinear time-delay systems. A numerically generated kernel, using the sum-of-squares decomposition of multivariate polynomials, is used in the construction of an appropriate Lyapunov-Krasovskii functional for stability analysis of the networks around an equilibrium point. This analysis translates to verifying equivalent LMI conditions. A delay-independent asymptotic stability of a second-order model of a gene regulatory network, taking into consideration multiple commensurate delays, is established.
Keywords: time-delay; cancer immunotherapy; gene-regulatory network; sum of squares