this paper addresses adaptive observer design problem for joint estimation of the states and unknown parameters for a class of nonlinear systems which satisfying one-sided lipschitz and quadratic inner bounded conditions. it’s shown that the stability of the proposed observer is related to finding solutions to a quadratic inequality consists of state and parameter errors. a coordinate transform...

We present and analyse two implicit methods for Ito stochastic differential equations (SDEs) with Poisson-driven jumps. The first method, SSBE, is a split-step extension of the backward Euler method. The second method, CSSBE, arises from the introduction of a compensated, martingale, form of the Poisson process. We show that both methods are amenable to rigorous analysis when a one-sided Lipsch...

Strong convergence results on tamed Euler schemes, which approximate stochastic differential equations with superlinearly growing drift coefficients that are locally one-sided Lipschitz continuous, are presented in this article. The diffusion coefficients are assumed to be locally Lipschitz continuous and have at most linear growth. Furthermore, the classical rate of convergence, i.e. one–half,...

We study the spreading of characteristics for a class of one-dimensional scalar conservation laws for which the ° ux function has one point of in° ection. It is well known that in the convex case the characteristic speed satis ̄es a one-sided Lipschitz estimate. Using Dafermos’ theory of generalized characteristics, we show that the characteristic speed in the non-convex case satis ̄es an Holder...

Abstract. We study stochastic equations of non-negative processes with jumps. The existence and uniqueness of strong solutions are established under Lipschitz and non-Lipschitz conditions. The comparison property of two solutions are proved under suitable conditions. The results are applied to stochastic equations driven by one-sided Lévy processes and those of continuous state branching proces...

In this paper, we establish sharp two-sided estimates for the Green functions of non-symmetric diffusions with measure-valued drifts in bounded Lipschitz domains. As consequences of these estimates, we get a 3G type theorem and a conditional gauge theorem for these diffusions in bounded Lipschitz domains. Informally the Schrödinger-type operators we consider are of the form L + μ · ∇ + ν where ...

This paper deals with state observer design problem for a class of nonlinear dynamical systems with interval time-varying delay that satisfies the one-sided Lipschitz condition. The systems under consideration include the well-studied Lipschitz system as a special case and possess inherent advantages with respect to conservativeness. By constructing a novel Lyapunov-Krasovskii functional and ut...