Related papers: Linearization and exponential stability
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…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
A linear system of difference equations and a nonlinear perturbation are considered, we obtain sufficient conditions to ensure the topological equivalence between them, namely, the linear part satisfies a property of dichotomy on the…
In many large systems, such as those encountered in biology or economics, the dynamics are nonlinear and are only known very coarsely. It is often the case, however, that the signs (excitation or inhibition) of individual interactions are…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable and the set of admissible switching signals obeys pre-specified restrictions on switches between the subsystems and dwell times on…
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…
In this paper, we prove a theorem of linearized asymptotic stability for fractional differential equations with a time delay. More precisely, using the method of linearization of a nonlinear equation along an orbit (Lyapunov's first…
Based on recent works on transverse exponential stability, we establish some necessary and sufficient conditions for the existence of a (locally) exponential synchronizing control law. We show that the existence of a structured synchronizer…
This paper investigates the exponential stability of abstract mean field systems in their synchronized state. We analyze stability by studying the linearized system and demonstrate the existence of an exponentially stable invariant…
We investigate how the following properties are related to each other: i)-A manifold is "transversally" exponentially stable; ii)-The "transverse" linearization along any solution in the manifold is exponentially stable; iii)-There exists a…
We consider semilinear evolution equations of the form $a(t)\partial_{tt}u + b(t) \partial_t u + Lu = f(x,u)$ and $b(t) \partial_t u + Lu = f(x,u),$ with possibly unbounded $a(t)$ and possibly sign-changing damping coefficient $b(t)$, and…
We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are…
We provide theoretical guarantees for recursive feasibility and practical exponential stability of the closed-loop system of a feedback linearizable nonlinear system when controlled by a robust data-driven nonlinear predictive control…
Plasma sheaths are inhomogeneous stationary states that form when a plasma is in contact with an absorbing wall. We prove linear and non linear stability of a kinetic sheath stationary state for a Vlasov-Poisson type system in a bounded…
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…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
We consider the Bresse model with three control boundary conditions. We prove the exponential stability of the system using the semigroup theory of linear operators and a result obtained by Pr\"uss.
The leading-order approximation to a Filippov system $f$ about a generic boundary equilibrium $x^*$ is a system $F$ that is affine one side of the boundary and constant on the other side. We prove $x^*$ is exponentially stable for $f$ if…
This paper investigates the stability of a class of differential systems time-changed by $E_{t}$ which is the inverse of a $\beta$-stable subordinator. In order to explore stability, a time-changed Gronwall's inequality and a generalized…
In this paper, the problem of partial stabilization of nonlinear systems along a given trajectory is considered. This problem is treated within the framework of stability of a family of sets. Sufficient conditions for the asymptotic…