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This paper presents a nonlinear dynamical model which consists the system of differential and operator equations. Here differential equation contains a nonlinear operator acting in Banach space, a nonlinear operator equation with respect to…
This paper presents a new paradigm to stabilize uncertain stochastic linear systems. Herein, second moment polytopic (SMP) systems are proposed that generalize systems with both uncertainty and randomness. The SMP systems are characterized…
We fill the two main remaining gaps in the full classification of non-degenerate planar traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under smooth perturbations. On one hand we…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
In this paper, a new global exponential stability criterion is obtained for a general multidimensional delay difference equation using induction arguments. In the cases that the difference equation is periodic, we prove the existence of a…
A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…
In this paper, we initiate the study of global stability for anisotropic systems of quasilinear wave equations. Equations of this kind arise naturally in the study of crystal optics, and they exhibit birefringence. We introduce a physical…
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…
We solve equations, describing in a simplified way the newtonian dynamics of a selfgravitating nonrotating spheroidal body after loss of stability. We find that contraction to a singularity happens only in a pure spherical collapse, and…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
Despite modular conditions to guarantee stability for large-scale systems have been widely studied, few methods are available to tackle the case of networks with multiple equilibria. This paper introduces small-gain like sufficient…
Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the…
The topological obstructions on the attitude space of a rigid body make global asymptotic stabilization impossible using continuous state-feedback. This paper presents novel algorithms to overcome such topological limitations and achieve…
We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
Estimating the Region of Attraction (RoA) for nonlinear dynamical systems is a fundamental problem in control theory, with direct implications for stability analysis and safe controller design. Traditional approaches rely on analytically…
Nonlinear underactuated systems such as two-wheeled inverted pendulums (TWIPs) exhibit a limited region of attraction (RoA), which defines the set of initial conditions from which the closed-loop system converges to the equilibrium. The RoA…
The neocortex has a remarkably uniform neuronal organization, suggesting that common principles of processing are employed throughout its extent. In particular, the patterns of connectivity observed in the superficial layers of the visual…
We present a theoretical and numerical framework to compute bifurcations of equilibria and stability of slender elastic rods. The 3D kinematics of the rod is treated in a geometrically exact way by parameterizing the position of the…
We show uniqueness and stability in $L^2$ and for all time for piecewise-smooth solutions to hyperbolic balance laws. We have in mind applications to gas dynamics, the isentropic Euler system and the full Euler system for a polytropic gas…