Related papers: On the Nonexistence of Quadratic Lyapunov Function…
Lyapunov-like characterizations for non-uniform in time and uniform robust global asymptotic stability of uncertain systems described by retarded functional differential equations are provided.
We show that for continuous time dynamical systems described by polynomial differential equations of modest degree (typically equal to three), the following decision problems which arise in numerous areas of systems and control theory…
This paper is devoted to the study of Lyapunov type inequalities for periodic conservative systems. The main results are derived from a previous analysis which relates the best Lyapunov constants to some especial (constrained or…
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…
We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the…
We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well known Lyapunov function of reaction…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
In this paper, we present sufficient conditions ensuring that the sum of the image of quadratic functions and the nonnegative orthant is convex. The hidden convexity of the trust-region problem with linear inequality constraints is…
We present a midpoint policy iteration algorithm to solve linear quadratic optimal control problems in both model-based and model-free settings. The algorithm is a variation of Newton's method, and we show that in the model-based setting it…
We study classes of weights ensuring the absence and presence of the Lavrentiev's phenomenon for double phase functionals upon every choice of exponents. We introduce a new sharp scale for weights for which there is no Lavrentiev's…
Some easily verifiable sufficient conditions for the nonexistence of iterative roots for multifunctions on arbitrary nonempty sets are presented. Typically if the graph of the multifunction has a distinguished point with a relatively large…
We study the phenomenon of lack of reversibility in molecular dynamics algorithms for the case of Wilson's lattice QCD. We demonstrate that the classical equations of motion that are employed in these algorithms are chaotic in nature. The…
Dealing with quadratic payments, marginal probability is usually considered ideally constant, maybe for the sake of initial simplicity. Considering the voting scenario depicted in "Quadratic Payments: A Primer" by Vitalik Buterin, firstly…
We prove the logarithmic Sarnak conjecture for sequences of subquadratic word growth. In particular, we show that the Liouville function has at least quadratically many sign patterns. We deduce the main theorem from a variant which bounds…
The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of…
In this paper, we construct an algorithm for minimising piecewise smooth functions for which derivative information is not available. The algorithm constructs a pair of quadratic functions, one on each side of the point with smallest known…
We review and give elementary proofs of Liouville type properties of harmonic and subharmonic functions in the plane endowed with a complete Riemannian metric, and prove a gap theorem for the possible growth of harmonic functions when this…
In this article, we provide a general strategy based on Lyapunov functionals to analyse global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is…
We study chaotic synchronization in a 5D Hindmarsh--Rose neuron model augmented with electromagnetic induction and a switchable memristive autapse. For two diffusively coupled identical neurons, we derive the transverse error dynamical…
An algorithm to characterize collective motion is presented, with the introduction of ``collective Lyapunov exponent'', as the orbital instability at a macroscopic level. By applying the algorithm to a globally coupled map, existence of…