On Stability Criteria of Third-Order Autonomous Nonlinear Differential Equations with Quasi-Derivatives

On Stability of Certain Class of 3-Rd Order Nonlinear Control Systems

“…Let us consider a system of differential equations of the first order expressed in the following matrix form [7] ),…”

“…where A is a real constant square matrix, ) (t B is a real square matrix depending on t only, such that If all eigenvalues of A have negative real parts, then the trivial solution o of [7] is asymptotically stable in Liapunov sense.…”

“…[ii] If at least one of eigenvalues of A has a positive real part, then the trivial solution o of [7] is instable in Liapunov sense. uniformly for all b t  .…”

“…Then we stated such results for autonomous nonlinear 3-rd equations (see (7)). The main aim of the presented article is to establish similar criteria for another class of third-order nonlinear differential equations with quasi-derivatives.…”

On Stability Criterion of 4-th Order Quasilinear Differential Equations with Quasiderivatives

“…It means that the classical stability criteria in this case cannot be used. For this reason, recently, several papers concerning the stability of differential equations with quasiderivatives have arisen -see, for example [4], [5], [6], where equations of the third order were investigated. This article deals with the asymptotic stability criterion, in the Liapunov sense, of arbitrary solutions of a certain class of ordinary differential equations -so called quasilinear 4-th order differential equations with quasiderivatives…”