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The Riccati inequality and equality are studied for infinite dimensional linear discrete time stationary systems with respect to the scattering supply rate. The results obtained are an addition to and based on our earlier work on the…

Functional Analysis · Mathematics 2016-09-02 D. Z. Arov , M. A. Kaashoek , D. R. Pik

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…

Dynamical Systems · Mathematics 2018-08-29 Mark A. Pinsky , Steve Koblik

A new approach with the Riccati equation method is used to obtain a non oscillation criterion for extended quasi linear Hamiltonian systems.

Classical Analysis and ODEs · Mathematics 2024-07-09 G. A. Grigorian

This contribution presents two exponential stability criteria for linear systems with multiple pointwise and distributed delays. These results (necessary and sufficient conditions) are given in terms of the delay Lyapunov matrix and the…

Dynamical Systems · Mathematics 2022-09-15 Alejandro Castaño , Carlos Cuvas , Alexey Egorov , Sabine Mondié

Methods from learning theory are used in the state space of linear dynamical and control systems in order to estimate the system matrices. An application to stabilization via algebraic Riccati equations is included. The approach is…

Dynamical Systems · Mathematics 2015-08-12 Fritz Colonius , Boumediene Hamzi

Stability of stationary solutions of parabolic equations is conventionally studied by linear stability analysis, Lyapunov functions or lower and upper functions. We discuss here another approach based on differential inequalities written…

Functional Analysis · Mathematics 2012-06-26 A. G. Ramm , V. Volpert

In this paper we present a direct formula for the solution of the general second order linear ordinary differential equation as our main result such that the parameters required for the formula are determined using another differential…

General Mathematics · Mathematics 2021-01-12 Rajnish Kumar Jha

We prove that Runge-Kutta (RK) methods for numerical integration of arbitrarily large systems of Ordinary Differential Equations are linearly stable. Standard stability arguments -- based on spectral analysis, resolvent condition or strong…

Numerical Analysis · Mathematics 2023-12-27 Eitan Tadmor

Some global existence criteria for quaternionic Riccati equations are established. Two of them are used to prove a completely non conjugation theorem for solutions of linear systems of ordinary differential equations.

Classical Analysis and ODEs · Mathematics 2019-09-20 G. A. Grigorian

This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…

Optimization and Control · Mathematics 2026-03-03 Matthieu Barreau , Carsten W. Scherer , Frederic Gouaisbaut , Alexandre Seuret

We study systems on time scales that are generalizations of classical differential or difference equations. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of…

Dynamical Systems · Mathematics 2016-06-07 Sergey Kryzhevich , Alexander Nazarov

Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…

Dynamical Systems · Mathematics 2025-08-25 Quinlan Leishman , Benjamin Webb

The paper is devoted to the study of stability of equilibrium solutions of a delay differential equation that models leukemia. The equation was previously studied in [5] and [6], where the emphasis is put on the numerical study of periodic…

Dynamical Systems · Mathematics 2010-01-27 Anca Veronica Ion

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…

Dynamical Systems · Mathematics 2016-12-14 Nicholas Apostolopoulos , Fernando Ortega , Grigoris Kalogeropoulos

An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. We introduce a new approach to solve a class of…

Probability · Mathematics 2012-03-20 Zhongmin Qian , Xun Yu Zhou

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…

Classical Analysis and ODEs · Mathematics 2010-09-16 Antonio Canada , Salvador Villegas

This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general…

Quantum Physics · Physics 2013-03-08 Matthew R. James , Ian R. Petersen , Valery Ugrinovskii

We propose a new algorithm for a broad class of periodic time-varying Stochastic Game-Theoretic Riccati Differential Equations arising in Zero-Sum Linear-Quadratic Stochastic Differential Games. The algorithm is constructed via dual-layer…

Numerical Analysis · Mathematics 2025-11-06 Yiyuan Wang

This paper proposes a novel iterative algorithm to compute the stabilizing solution of regime-switching stochastic game-theoretic Riccati differential equations with periodic coefficients. The method decomposes the original complex…

Numerical Analysis · Mathematics 2025-11-11 Yiyuan Wang

Direct solution of simultaneous linear equations is regarded to be slow for large systems of equations and requires special treatment to avoid numerical instability. A new method is proposed that addresses the numerical instability without…

Numerical Analysis · Mathematics 2011-05-02 Anoosh Abdy