Related papers: Lyapunov and Riccati Equations from a Positive Sys…
In this paper, we describe sufficient conditions when block-diagonal solutions to Lyapunov and $\mathcal{H}_{\infty}$ Riccati inequalities exist. In order to derive our results, we define a new type of comparison systems, which are positive…
In the present paper, a novel vector field decomposition based approach for constructing Lyapunov functions is proposed. For a given dynamical system, if the defining vector field admits a decomposition into two mutually orthogonal vector…
Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for…
In the present paper we give a positive answer to some questions posed by Viana on the existence of positive Lyapunov exponents for Hamiltonian linear differential systems. We prove that there exists an open and dense set of Hamiltonian…
It is proved that the members of the Riccati hierarchy, the so-called Riccati chain equations, can be considered as particular cases of projective Riccati equations, which greatly simplifies the study of the Riccati hierarchy. This also…
The paper introduces and studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. A generalization of Perron Frobenius theory is developed in this differential framework to…
The Riccati equation method is used to establish a new stability criteria for linear systems of ordinary differential equations. Two examples are presented in which the obtained result is compared with the results obtained by the Lyapunov…
This paper is concerned with relationships of Lyapunov exponents with sensitivity and stability for non-autonomous discrete systems. Some new concepts are introduced for non-autonomous discrete systems, including Lyapunov exponents, strong…
The Riccati equation method and an approach of the use of unknown factors is used to establish oscillation, suboscillation and nonoscillation criteria for linear systems of ordinary differential equations. A necessary condition for Lyapunov…
Inspired by the widespread concept of Lyapunov-Krasovskii functionals of complete type, this article proposes an alternative class of functionals, termed Lyapunov-Krasovskii functionals of robust type. Their construction aims at improving…
We consider systems of parabolic linear equations, subject to Neumann boundary conditions on bounded domains in $\mathbb{R}^d$, that are coupled by a matrix-valued potential $V$, and investigate under which conditions each solution to such…
We study in this paper a forward-backward-forward dynamical system for solving a mixed variational inequality problem in a real Hilbert space. For the convergence analysis of our proposed system, we apply the Lyapunov analysis to obtain the…
The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use successive approximation of solutions, ensuring its positivity. To…
We consider $k$-positive linear systems, that is, systems that map the set of vectors with up to $k-1$ sign variations to itself. For $k=1$, this reduces to positive linear systems. It is well-known that stable positive linear time…
Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and $H^\infty$ control theory. In this work, we study the properties of one type of discrete-time algebraic Riccati…
Ergodic properties of rational maps are studied, generalising the work of F.\ Ledrappier. A new construction allows for simpler proofs of stronger results. Very general conformal measures are considered. Equivalent conditions are given for…
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…
In this paper we consider the existence of positive solutions for a singular elliptic problem involving an asymtotically linear nonlinearity and depending on one positive parameter. Using variational methods, together with comparison…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in…