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Practical stability of discontinuous systems with external perturbations. (English) Zbl 0535.34039
Summary: In this paper, we consider the discontinuous system $$\dot x=f(t,x)$$ and at the same time consider the perturbed discontinuous system $$\dot x=f(t,x)+R(t,x)$$, where $$x\in E^ n$$, $$\dot x=dx/dt$$ and $$t\in [0,\infty)$$. In this article the definition of practical stability is given and many sufficient conditions which ensure practical stability and practical unstability are obtained and proved. In order to demonstrate the methods involved, some examples are considered.

##### MSC:
 34D20 Stability of solutions to ordinary differential equations 34D10 Perturbations of ordinary differential equations
##### Keywords:
perturbed discontinuous system; practical stability