DETERMINATION OF STABILITY BY LINEAR APPROXIMATION OF A PERIODIC SOLUTION OF A SYSTEM OF DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS RIGHT-HAND SIDES

It is the purpose of this paper to analyse the stability of a periodic solution zi=z˜i(t)[z˜i(t+τ)≡z˜i(t)] of system (0.1) when the right-hand sides fi are discontinuous at some points of the integral curve zi = z˜i(t). An explanation of the meaning of the linear approximation for this ‘discontinuous’ case is offered, and theorems, analogous to those of Liapounoff on stability by linear approximation in the continuous case, are presented.