Related papers: Unstable Limit Cycles Estimation from Small Pertur…
This article is devoted to the stabilization of two underactuated planar systems, the well-known straight beam-and-ball system and an original circular beam-and-ball system. The feedback control for each system is designed, using the Jordan…
Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the…
Engineered systems naturally experience large disturbances that can disrupt desired operation because the system may fail to recover to a stable equilibrium point. It is valuable to determine the mechanism of instability when the system is…
Driven many-particle systems with nonlinear interactions are known to often display multi-stability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models,…
Recent studies suggest that unstable, non-chaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role…
In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition…
A limit cycle is a self-sustained periodic motion appearing in autonomous ordinary differential equations. As the period of the limit cycle is a-priori unknown, it is challenging to find them as stationary states of a rotating ansatz.…
We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available…
We present a method to detect the unstable periodic orbits of a multidimensional chaotic dynamical system. Our approach allows us to locate in an efficient way the unstable cycles of, in principle, arbitrary length with a high accuracy.…
In the context of studying periodic processes, this paper investigates first under which conditions switching affine systems in the plane generate stable limit cycles. Based on these conditions, a design methodology is proposed by which the…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous applied and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which…
We outline a method for controlling the location of stable and unstable manifolds in the following sense. From a known location of the stable and unstable manifolds in a steady two-dimensional flow, the primary segments of the manifolds are…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such…
An experimental method has been developed to locate unstable equilibria of nonlinear structures quasi-statically. The technique involves loading a structure by application of either a force or a displacement at a main actuation point, while…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
We consider the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems, with linearly parameterised uncertainty. Assuming a region of the state space…
A novel perturbation method for the stabilization of unstable intermediate states of hysteresis loop (i.e. S-shaped curve) is proposed. This method only needs output signals of the system to construct the perturbation form without…