Related papers: Stabilization of slow-fast systems at fold points
Here we deal with the stabilization problem of non-diagonal systems by boundary control. In the studied setting, the boundary control input is subject to a constant delay. We use the spectral decomposition method and split the system into…
Motivated by the normal form of a fast-slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an application of the explicit Euler method. Tracking…
The computational singular perturbation (CSP) method is an algorithm which iteratively approximates slow manifolds and fast fibers in multiple-timescale dynamical systems. Since its inception due to Lam and Goussis, the convergence of the…
We study fast-slow maps obtained by discretization of planar fast-slow systems in continuous time. We focus on describing the so-called delayed loss of stability induced by the slow passage through a singularity in fast-slow systems. This…
We consider several classes of degenerate hyperbolic equations involving delay terms and suitable nonlinearities. The idea is to rewrite the problems in an abstract way and, using semigroup theory and energy method, we study well posedness…
We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…
This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate…
We consider the problem of optimizing the steady state of a dynamical system in closed loop. Conventionally, the design of feedback optimization control laws assumes that the system is stationary. However, in reality, the dynamics of the…
A control design approach is developed for a general class of uncertain strict-feedback-like nonlinear systems with dynamic uncertain input nonlinearities with time delays. The system structure considered in this paper includes a nominal…
Topological point defects on orientationally ordered spheres, and on deformable fluid vesicles have been partly motivated by their potential applications in creating super-atoms with directional bonds through functionalization of the…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
We extend the recently developed discrete geometric singular perturbation theory to the non-normally hyperbolic regime. Our primary tool is the Takens embedding theorem, which provides a means of approximating the dynamics of particular…
We study sufficient conditions for stability and recurrence in a class of singularly perturbed stochastic hybrid dynamical systems. The systems considered combine multi-time-scale deterministic continuous-time dynamics, modeled by…
We design observer-based controllers to stabilise abstract linear boundary control systems on Hilbert spaces. Our main results introduce conditions for exponential, strong, and polynomial stability, and establish external well-posedness of…
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…
For a wide class of second order nonlinear non-autonomous models, we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal, allows to stabilize unstable motions…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
This paper proposes a new methodology for design of a stabilizing control law for multi-input linear systems with time-varying, singular gains on the control. The results presented here assume the control gain to satisfy persistence of…
In this paper we study coupled fast-slow ordinary differential equations (ODEs) with small time scale separation parameter $\epsilon$ such that, for every fixed value of the slow variable, the fast dynamics are sufficiently chaotic with…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…