A piecewise affine (PWA) model of a gene regulatory network is considered. After an introduction to the model, the problem of finding a generally non-smooth function V (x) which is non increasing along the system trajectories is addressed and a way of solving it is given in terms of an LMI's feasibility problem. The presence of sliding modes in the system is explicitly considered and conditions of non-increase of V (x) along these are stated in terms of LMIs. Finally, we present an example which show the resulting V (x) obtained by solving the feasibility problem described.
On piecewise quadratic Lyapunov functions for piecewise affine models of gene regulatory networks / Pasquini, Mirko; Angeli, David. - ELETTRONICO. - (2018), pp. 1071-1076. ( IEEE Conference on Decision and Control).
On piecewise quadratic Lyapunov functions for piecewise affine models of gene regulatory networks
Angeli, David
2018
Abstract
A piecewise affine (PWA) model of a gene regulatory network is considered. After an introduction to the model, the problem of finding a generally non-smooth function V (x) which is non increasing along the system trajectories is addressed and a way of solving it is given in terms of an LMI's feasibility problem. The presence of sliding modes in the system is explicitly considered and conditions of non-increase of V (x) along these are stated in terms of LMIs. Finally, we present an example which show the resulting V (x) obtained by solving the feasibility problem described.
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