We offer a simple proof of the Lyapunov finite-time stability theorem for Filippov systems which does not use any generalized derivatives to differentiate the composition of the Lyapunov function with absolutely continuous solutions.doi:10.1016/j.crma.2017.02.003Makarenkov...
Proof of a certain conjecture on the stability of linear discrete systemsThe proof of a previously published conjecture on the stability of linear discrete systems is obtained using Lyapunov''s second stability theorem.doi:10.1080/00207178208932915...
The proofs are direct in the sense that they do not resort to any existing result in systems theory, such as Lyapunov theory, passivity theory or the small-gain theorem. Instead, the proofs refer to the asymptotic properties of block-Toeplitz matrices. One major advantage of the new proof ...
Lyapunov's result on a sharp integral estimate for the zero stability zone of the Hill equation is well known. It was announced in [1] that the integral over the period in Lyapunov's inequality can be replaced by the integral over an arbitrary half-period. Below we prove this assertion....
MATHEMATICAL formulasMATHEMATICAL modelsWe give a short, elementary proof of the Greenlee's stability theorem for linear conservative gyroscopic systems. The proof is based on the direct method of Lyapunov.BULATOVI, R. M.Mathematica Montisnigri
ISS small-gain theoreminput-to-state stable small-gain theoremLyapunov-type proofstability criterioninterconnected nonlinear systemsThis paper presents a Lyapunov-type proof of the input-to-state stable (ISS) small-gain theorem. The proof given in this paper demonstrates how to construct a Lyapunov ...
At the first step, using Lyapunov’s direct method, a non-linear state feedback is selected so that without any need to apply identification techniques, in despite of the uncertain parameters existence in the system state equations, the asymptotic stability of the general Lorenz sy...
Diagonal stabilityCommon quadratic Lyapunov functionsCopositive diagonal Lyapunov functionsWe revisit the theorem of Barker, Berman and Plemmons on the existence of a diagonal quadratic Lyapunov function for a stable linear time-invariant (LTI) dynamical system [G.P. Barker, A. Berman, R.J. Plemmons...
In this article, some new Lyapunov-type inequalities for a class of fractional boundary value problems are established by use of the nonsymmetry property of Green’s function corresponding to appropriate boundary conditions. Keywords: Lyapunov-type inequality; Green’s function; boundary value problem ...