# American Institute of Mathematical Sciences

July  2017, 22(5): 1977-1986. doi: 10.3934/dcdsb.2017116

## On practical stability of differential inclusions using Lyapunov functions

 Taras Shevchenko National University of Kyiv, Department of Computer Science and Cybernetics, Volodymyrska Str. 60,01033, Kyiv, Ukraine

Received  January 2016 Revised  February 2016 Published  March 2017

In this paper we consider the problem of practical stability for differential inclusions. We prove the necessary and sufficient conditions using Lyapunov functions. Then we solve the practical stability problem of linear differential inclusion with ellipsoidal righthand part and ellipsoidal initial data set. In the last section we apply the main result of this paper to the problem of practical stabilization.

Citation: Volodymyr Pichkur. On practical stability of differential inclusions using Lyapunov functions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 1977-1986. doi: 10.3934/dcdsb.2017116
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