Related papers: Well-posedness and stability of boundary delay equ…
While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of…
We analyse dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a previous known sufficient condition for exponential stability with respect to the C^1-norm is optimal. In particular a known…
We consider several classes of degenerate hyperbolic equations involving delay terms and suitable nonlinearities. The idea is to rewrite the problems in an abstract way and, using semigroup theory and energy method, we study well posedness…
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…
We investigate the finite time stability property of one-dimensional nonautonomous initial boundary value problems for linear decoupled hyperbolic systems with nonlinear boundary conditions. We establish sufficient and necessary conditions…
A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is…
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…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and…
This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
This paper addresses the qualitative theory of mixed-order positive linear coupled systems with bounded or unbounded delays. First, we introduce a general result on the existence and uniqueness of solutions to mixed-order linear coupled…
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…
This paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems, and establishes the relationship between the eigenvalue distribution and delay-independent stability of neutral…
In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…
In this paper, we establish a necessary and sufficient stability condition for a class of two coupled first-order linear hyperbolic partial differential equations. Through a backstepping transform, the problem is reformulated as a stability…
In this paper, we establish the existence of a positive, bounded solution for a class of parabolic partial differential equations with nonlinear boundary conditions, where the boundary conditions depend on the solution on the boundary at a…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global…
We study the stability of general $n$-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first…