Related papers: Delay periodic Lyapunov equation
In this paper we show that the existence of a Lyapunov-Krasovskii functional is necessary and sufficient condition for the uniform global asymptotic stability and the global exponential stability of time-invariant systems described by…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
In this paper we are concerned with the stability of equilibrium solutions of periodic Hamiltonian systems with one degree of freedom in the case of degeneracy, which means that the characteristic exponents of the linearized system have…
We establish a unified theoretical framework that connects classical orthogonal polynomial systems to matrix Lyapunov equations through the fundamental physics of energy dissipation in stochastic dynamical systems. Starting from the energy…
Koopman operator provides a general linear description of nonlinear systems, whose estimation from data (via extended dynamic mode decomposition) has been extensively studied. However, the elusiveness between the Koopman spectrum and the…
We analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are…
In this technical note, we consider the stability properties of a viscously damped Timoshenko beam equation with spatially varying parameters. With the help of the port-Hamiltonian framework, we first prove the existence of solutions and…
In this study, we focus on the existence of a periodic solution for the neutral nonlinear dynamic systems with delay% \[ x^{\Delta}(t)=A(t)x(t)+Q^{\Delta}\left(t,x\left(\delta_{-}(s,t)\right) \right)…
In this work we investigate some asymptotic properties of an age-structured Lotka-Volterra model, where a specific choice of the functional parameters allows us to formulate it as a delayed problem, for which we prove the existence of a…
We study exponential stability for a kind of neural networks having time-varying delay. By extending the auxiliary function-based integral inequality, a novel integral inequality is derived by using weighted orthogonal functions of which…
We consider a one-parameter family of beam equations with Hamiltonian non-linearity in one space dimension under periodic boundary conditions. In a unified functional framework we study the long time evolution of initial data in two…
This paper proposes methods to handle the problem of delay range stability analysis for a linear coupled differential-difference system (CDDS) with distributed delays subject to dissipative constraints. The model of linear CDDS contains…
In this paper, we consider the stability of discrete-time linear switched systems with a common non-strict Lyapunov matrix.
A new necessary and sufficient stability test in a tractable number of operations for linear neutral-type delay systems is introduced. It is developed in the Lyapunov-Krasovskii framework via functionals with prescribed derivatives. The…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
We consider the stability analysis of a large class of linear 1-D PDEs with polynomial data. This class of PDEs contains, as examples, parabolic and hyperbolic PDEs, PDEs with boundary feedback and systems of in-domain/boundary coupled…
This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…
In this work, we address the problem of finite-time stabilization for a class of bilinear system. We propose a decomposition-based approach in which the nominal system is split into two subsystems, one of which is inherently finite-time…
We revisit the equilibrium one-dimensional $\phi^4$ model from the dynamical systems point of view. We find an infinite number of periodic orbits which are computationally stable. At the same time some of the orbits are found to exhibit…
Lyapunov functions play a vital role in the context of control theory for nonlinear dynamical systems. Besides its classical use for stability analysis, Lyapunov functions also arise in iterative schemes for computing optimal feedback laws…