Related papers: Diagonal Riccati Stability and Applications
We study the global stability of generalized Lotka-Volterra systems with generalized polynomial right-hand side, without restrictions on the number of variables or the polynomial degree, including negative and non-integer degree. We…
We study the stability of switched systems where the dynamic modes are described by systems of higher-order linear differential equations not necessarily sharing the same state space. Concatenability of trajectories at the switching…
Some properties of global solution of scalar Riccati equation are studied. On the basis of these properties using the Whiburn's and Leighton - Nehary's theorems some oscillatory and criteria are proved for second order linear systems of…
Three comparison criteria are obtained for second order Riccati equations. On the basis of these criteria some global existence theorems are proved mentioned equations. The results obtained are used to derive a non oscillation criterion for…
The main purpose of this paper is to present a general method for the controllability of the stability of a system of fractional-order differential equations around its equilibrium states. This method is applied to analyze and control the…
In this paper, we consider nonsymmetric solutions to certain Lyapunov and Riccati equations and inequalities with coefficient matrices corresponding to cone-preserving dynamical systems. Most results presented here appear to be novel even…
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides…
In this paper we consider a class of systems of two coupled real scalar fields in bidimensional spacetime, with the main motivation of studying classical or linear stability of soliton solutions. Firstly, we present the class of systems and…
The focal point of this paper is to provide some simple and efficient criteria to judge the ${\cal D}$-stability of two families of polynomials, i.e., an interval multilinear polynomial matrix family and a polytopic polynomial family.…
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…
It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…
In this paper, I computed the second variation formula of the generalized Einstein-Hilbert functional and prove that a Bismut-flat, Einstein manifold is linearly stable under some curvature assumption. In the last part of the paper, I prove…
The geometric theory of Lie systems is used to establish integrability conditions for several systems of differential equations, in particular some Riccati equations and Ermakov systems. Many different integrability criteria in the…
We use a new approach with a matrix transformation to obtain a new global solvability criterion for matrix Riccati equations. The proven theorem completes an well known result in directions of extension of classes of coefficient of…
The concept of matrix D-stability plays an important role in applications, ranging from economic and biological system models to decentralized control. Here we provide necessary and sufficient Lyapunov-type conditions for the robust (block)…
This note explores the extension of D-stability to non-square matrices, applicable to distributed/decentralized controllability analysis. We first present a definition of D-stability for non-square matrices, directly extending from square…
We associate to an arbitrary $\mathbb Z$-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati…
Generalized mass-action systems are power-law dynamical systems arising from chemical reaction networks. Essentially, every nonnegative ODE model used in chemistry and biology (for example, in ecology and epidemiology) and even in economics…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
We study the equilibria of a large Lokta-Volterra system of coupled differential equations in the case where the interaction coefficients form a large random matrix. In the case where this random matrix follows an elliptic model , we study…