Stability with regime switching

The purpose of this paper is to analyze the stability of systems of piecewise continuous differential equations, and to apply the results to a disequilibrium economic model. The discontinuity problem appears in disequilibrium models because of the so-called “short-side” rule. The concept of Filippov solution makes it possible to analyze the dynamic evolution of such a model. This paper demonstrates that (i) stability conditions for each subsystem are neither necessary nor sufficient for overall stability, except in special cases such as a system of linear differential equations in R² with two regimes separated by a linear boundary; (ii) several sufficient conditions for overall stability with many regimes are available; and (iii) stability theorems with regime switching are useful for disequilibrium economic models with several regimes.