Singular extensions of discontinuous systems and stability. (Russian) Zbl 0715.34102

Fridman, L. M.

Differ. Uravn. 26, No. 10, 1759-1765 (1990).

In his former paper [ibid. 22, No.8, 1461-1463 (1986; Zbl 0654.34055)] the author introduced a notion of solution for a system of differential equations with discontinuous right-hand sides exhibiting the so called “sliding regime” by replacing the system by a singularly perturbed one. In the present paper, he gives sufficient conditions under which (a) stability of a solution of the shortened system implies stability of the corresponding solution of the singularly perturbed system, and (b) there exists an orbitally asymptotically stable periodic solution of the singularly perturbed system.

Reviewer: J.Jarník

MSC:

34D15	Singular perturbations of ordinary differential equations
34C25	Periodic solutions to ordinary differential equations

Keywords:

orbitally asymptotically stable periodic solution; singularly perturbed system