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This paper is concerned with incremental stability properties of nonlinear systems. We propose conditions to compute an upper bound on the incremental L2-gain and to assess incremental asymptotic stability of piecewise-affine (PWA) systems.…
In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems…
The problem of estimating the L\'evy density of a partially observed multidimensional affine process from low-frequency and mixed-frequency data is considered. The estimation methodology is based on the log-affine representation of the…
We address the problem of Lyapunov function construction for a class of continuous-time Markov chains with affine transition rates, typically encountered in stochastic chemical kinetics. Following an optimization approach, we take advantage…
Isotonic regression provides a flexible, tuning-free approach to estimating monotonic functions without imposing global curvature constraints, yet the estimated regression function is inherently a step function. This paper addresses a key…
A fruitful approach to study stability of switched systems is to look for multiple Lyapunov functions. However, in general, we do not yet understand the interplay between the desired stability certificate, the template of the Lyapunov…
A class of piecewise affine hyperbolic maps on a bounded subset of the plane is considered. It is shown that if a map from this class is sufficiently area-expanding then almost surely this map has an absolutely continuous invariant measure.
This paper is concerned with the problem of finding a quadratic common Lyapunov function for a family of stable linear systems. We present gradient iteration algorithms which give deterministic convergence for finite system families and…
We survey the main results of approximation theory for adaptive piecewise polynomial functions. In such methods, the partition on which the piecewise polynomial approximation is defined is not fixed in advance, but adapted to the given…
Spectral polynomial approximation of smooth functions allows real-time manipulation of and computation with them, as in the Chebfun system. Extension of the technique to two-dimensional and three-dimensional functions on hyperrectangles has…
We study fast approximation of integrals with respect to stationary probability measures associated to iterated functions systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on the…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
We propose a composite Lyapunov framework for nonlinear autonomous systems that ensures strict decay through a pair of differential inequalities. The approach yields integral estimates, quantitative convergence rates, vanishing of…
We propose a moving horizon estimation scheme for joint state and parameter estimation for nonlinear uncertain discrete-time systems. We establish robust exponential convergence of the combined estimation error subject to process…
Reachability analysis of compositional hybrid systems, where individual components are modeled as hybrid automata, poses unique challenges. In addition to preserving the compositional semantics while computing system behaviors, algorithms…
Inspired by the widespread concept of Lyapunov-Krasovskii functionals of complete type, this article proposes an alternative class of functionals, termed Lyapunov-Krasovskii functionals of robust type. Their construction aims at improving…