In this paper, we describe our application of SPIN [1] to model an algorithm used to synchronize the clocks of modules that provide periodic real-time communication over a network. We used the SPIN model to check certain performance properties of the system; in particular, we were able to verify that the algorithm achieves synchronization within a time bound, even in the presence of certain typ...

We discuss the problem of semi-globally asymptotically stabilizing general nonlinear discretetime systems in the presence of data-rate constraints under the stabilizability assumption only. The proposed solution relies on a simple result on asymptotic estimation for nonlinear systems under data-rate constraints, which holds for trajectories confined within a known bounded region of the state sp...

We study regularity of mild and strong solutions for an abstract mathematical model of a flexible space structure under appropriate initial conditions. We apply our results showing qualitative properties of the trajectories in case of the negative Laplacian operator.

We consider the concept of Reachability for systems described by PMDs, generalizing various known results from the theory of generalized state space systems using time domain analysis,which takes into account the finite and infinite pole-zero structure of the associated matrix. We extend also the theory of admissible initial conditions and we introduce the concept of Reachable subspace for PMDs...

The famous Lorenz system is studied and analyzed for a particular set of parameters originally proposed by Lorenz. With those parameters, the system has a single globally attracting strange attractor, meaning that almost all initial conditions in its 3D state space approach the attractor as time advances. However, with a slight change in one of the parameters, the chaotic attractor coexists wit...

We investigate the properties of the Ma–Trudinger–Wang nonlocal curvature tensor in the case of surfaces. In particular, we prove that a strict form of the Ma–Trudinger–Wang condition is stable under C perturbation if the nonfocal domains are uniformly convex; and we present new examples of positively curved surfaces which do not satisfy the Ma–Trudinger–Wang condition. As a corollary of our re...

In this paper, we are concerned with the fast solvers for higher order finite element discretizations of H(div)-elliptic problem. We present the preconditioners for the first family and second family of higher order divergence conforming element equations, respectively. By combining the stable decompositions of two kinds of finite element spaces with the abstract theory of auxiliary space preco...

be the set of k observations. Finding xak, the estimate or analysis of the state space xk, given Zk and the initial conditions is called the filtering problem. When the dynamic model for the process, f(·), and for the measurements, h(·), are linear, and the random components x0, wk, vk are uncorrelated Gaussian random vectors, then the solution is given by the classical Kalman filter equations ...

We study the controllability properties of the class of stochastic differential systems characterized by a linear controlled diffusion perturbed by a smooth, bounded, uniformly Lipschitz nonlinearity. We obtain conditions that guarantee the weak and strong controllability of the system. Also, given any open set in the state space we construct a control, depending only on the Lipschitz constant ...