This paper revisits the problems of estimating the position of an object moving in n (≥ 2)-dimensional Euclidean space using velocity measurements and either direction or range measurements of one or multiple source points. The proposed solutions exploit the Continuous Riccati Equation (CRE) to calculate observer gains yielding global exponential stability of zero estimation errors, even in the...

Abstract In this paper, we consider the uniform norm discretization problem for general real multivariate exponential sums $$p({{\mathbf{w}}})=\sum _{0\le j\le n}c_je^{\langle \mu _j, {{\mathbf{w}}}\rangle }, \;\;\mu {{\mathbf{w}}}\in \mathbb {R}^d$$ p ( w ) <...

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...