102 Feedback Control in Systems Biology
solution to the feasibility P roblem 2 is then given by
γ = 0.1194, P =
0.0319 −0.0027 −0.0464
−0.0027 4.194 7.259
−0.0464 7.259 182.26
,
which can be readily obtained by numerically solving the problem using the
YALMIP [35] package or the MATLAB
r
LMI Toolbox [36]. Thus, we can
conclude that the box R belongs to the region of attraction of E
3
. This implies
that every trajectory starting from an initial condition included in R (such
as, for example, those shown in Fig. 3.13) converges to E
3
.
Optimis ation of the therapeutic treatment
Changes in the hemodynamic per fusion of the tumour, radiation or chemother-
apy may induce stochastic perturbations of the state variables around the
equilibrium point E
3
, thus leading ...