Related papers: Lyapunov equation in open quantum systems and non-…
It is well-known that the Lyapunov exponent plays a fundamental role in dynamical systems. In this note, we propose an alternative definition of Lyapunov exponent in terms of Lipschitz maps, which are not necessarily differentiable. We show…
This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic…
This paper deals with the robust stability analysis of linear systems, subject to time-varying parameters. The Parameter Dependent Lyapunov Function are considered, assuming that the temporal derivative of the parameters are bounded. Some…
Despite their spectacular progress, language models still struggle on complex reasoning tasks, such as advanced mathematics. We consider a long-standing open problem in mathematics: discovering a Lyapunov function that ensures the global…
Hyperbolic systems in one dimensional space are frequently used in modeling of many physical systems. In our recent works, we introduced time independent feedbacks leading to the finite stabilization for the optimal time of homogeneous…
A Lyapunov-based control design for natural trajectory-tracking problems is analyzed for quantum states where the analysis in the generic case is not applicable. Using dynamical systems tools we show almost global asymptotic stability for…
A quantum system whose internal Hamiltonian is not strongly regular or/and control Hamiltonians are not full connected, are thought to be in the degenerate cases. In this paper, convergence problems of the multi-control Hamiltonians closed…
A new universality of Lyapunov spectra {\lambda_i} is shown for Hamiltonian systems. The universality appears in middle energy regime and is different from another universality which can be reproduced by random matrices in the following two…
This paper considers the problem of finite-time stability for stochastic nonlinear systems. A new Lyapunov theorem of stochastic finite-time stability is proposed, and an important corollary is obtained. Some comparisons with the existing…
As is widely recognized in Lyapunov analysis, linearized Hamilton's equations of motion have two marginal directions for which the Lyapunov exponents vanish. Those directions are the tangent one to a Hamiltonian flow and the gradient one of…
Quadratic Lyapunov function has been widely used in the analysis of linear time invariant (LTI) systems ever since it has shown that the existence of such quadratic Lyapunov function certifies the stability of the LTI system. In this work,…
The Lyapunov spectrum corresponding to a periodic orbit for a two dimensional many particle system with hard core interactions is discussed. Noting that the matrix to describe the tangent space dynamics has the block cyclic structure, the…
In this note, a novel methodology that can extract a number of analysis results for linear time-invariant systems (LTI) given only a single trajectory of the considered system is proposed. The superiority of the proposed technique relies on…
This paper is devoted to provide some new results on Lyapunov type inequalities for the periodic boundary value problem at higher eigenvalues. Our main result is derived from a detailed analysis on the number and distribution of zeros of…
This paper presents a new method for synthesizing stochastic control Lyapunov functions for a class of nonlinear stochastic control systems. The technique relies on a transformation of the classical nonlinear Hamilton-Jacobi-Bellman partial…
If an open quantum system is initially uncorrelated from its environment, then its dynamics can be written in terms of a Lindblad-form master equation. The master equation is divided into a unitary piece, represented by an effective…
This paper is devoted to the study of $L_p$ Lyapunov-type inequalities for linear systems of equations with Neumann boundary conditions and for any constant $p \geq 1$. We consider ordinary and elliptic problems. The results obtained in the…
Time bounded reachability is a fundamental problem in model checking continuous-time Markov chains (CTMCs) and Markov decision processes (CTMDPs) for specifications in continuous stochastic logics. It can be computed by numerically solving…
The tangent dynamics of the Lyapunov modes and their dynamics as generated numerically - {\it the numerical dynamics} - is considered. We present a new phenomenological description of the numerical dynamical structure that accurately…
Recently the bound on the Lyapunov exponent $\lambda_L \le 2\pi T/ \hbar$ in thermal quantum systems was conjectured by Maldacena, Shenker, and Stanford. If we naively apply this bound to a system with a fixed Lyapunov exponent $\lambda_L$,…