Stabilization analysis for economic compartmental switched systems based on quadratic Lyapunov function

The compartmental model is one of the important applications in economic and social dynamic systems which are made of numbers of units-subsystems. Stabilization of economic compartmental switched systems with compartmental subsystems is studied in this paper. A quadratic Lyapunov function is introduced to construct switching law in order to stabilize these kinds of mathematical economic and social models. Necessary and sufficient conditions of stabilization are presented for both asynchronous and synchronous switching. Precisely, after a proper change in state space, stabilization conditions can be expressed in terms of matrix inequalities. At the same time, definitions, theorems and corollaries as well as a detailed simulation result of one example are presented to show the effectiveness of the main result obtained.