Related papers: Dynamical Systems with a Cyclic Sign Variation Dim…
We consider the data-driven stabilization of discrete-time linear time-varying systems. The controller is defined as a linear state-feedback law whose gain is adapted to the plant changes through a data-based event-triggering rule. To do…
Many nonlinear dynamical systems exhibit symmetry, affording substantial benefits for control design, observer architecture, and data-driven control. While the classical notion of group invariance enables a cascade decomposition of the…
We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two topological properties for set-valued functions and…
We investigate the approach of time-dependent variational principle (TDVP) for the one-dimensional spin-$J$ PXP model with detuning, which is relevant for programmable Rydberg atom arrays. The variational manifold is chosen as the minimally…
We present an algorithm to compute stabilizing minimum dwell times for discrete-time switched linear systems without the explicit knowledge of state-space models of their subsystems. Given a set of finite traces of state trajectories of the…
A novel method for stability and instability study of autonomous dynamical systems using the flow and divergence of the vector field is proposed. A relation between the method of Lyapunov functions and the proposed method is established.…
A new Small-Gain Theorem is presented for general nonlinear control systems. The novelty of this research work is that vector Lyapunov functions and functionals are utilized to derive various input-to-output stability and input-to-state…
We study dimension theory for dissipative dynamical systems, proving a conditional variational principle for the quotients of Birkhoff averages restricted to the recurrent part of the system. On the other hand, we show that when the whole…
The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all…
By means of the linear parameter-varying (LPV) Fundamental Lemma, we derive novel data-driven predictive control (DPC) methods for LPV systems. In particular, we present output-feedback and state-feedback-based LPV-DPC methods with terminal…
A Path-Complete Lyapunov Function is an algebraic criterion composed of a finite number of functions, called its pieces, and a directed, labeled graph defining Lyapunov inequalities between these pieces. It provides a stability certificate…
We study in detail the role of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discussed in several atmospheric science applications. The…
In many dynamical systems in nature, the law of the dynamics changes along with the temporal evolution of the system. These changes are often associated with the occurrence of certain events. The timing of occurrence of these events…
Symmetric matrix-valued dynamical systems are an important class of systems that can describe important processes such as covariance/second-order moment processes, or processes on manifolds and Lie Groups. We address here the case of…
In relativistic kinetic theory, the one-particle distribution function is approximated by an asymptotic perturbative power series in Knudsen number which is divergent. For the Bjorken flow, we expand the distribution function in terms of…
This paper provides sufficient conditions for stability of switched linear systems under dwell-time switching. Piece-wise quadratic functions are utilized to characterize the Lyapunov functions and bilinear matrix inequalities conditions…
It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory we derive numerical and in particular…
In this paper, a necessary and sufficient condition for the stability of Lyapunov exponents of linear differential system are proved in the sense that the equations satisfy the weaker form of integral separation instead of its classical…
With a scalar potential and a bivector potential, the vector field associated with the drift of a diffusion is decomposed into a generalized gradient field, a field perpendicular to the gradient, and a divergence-free field. We give such…
In structural dynamics, energy dissipative mechanisms with non-viscous damping are characterized by their dependence on the time-history of the response velocity, mathematically represented by convolution integrals involving hereditary…