Related papers: Stability of switched linear differential systems
This paper is concerned with the stability problem for the planar linear switched system $\dot x(t)=u(t)A_1x(t)+(1-u(t))A_2x(t)$, where the real matrices $A_1,A_2\in \R^{2\times 2}$ are Hurwitz and $u(\cdot) [0,\infty[\to\{0,1\}$ is a…
Recent works have shown that the $L_1$ and $L_\infty$-gains are natural performance criteria for linear positive systems as they can be characterized using linear programs. Those performance measures have also been extended to linear…
Characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature. This article collects a multitude of stabilizing switching signals under an…
We give a sufficient condition for exponential stability of a network of lossless telegrapher's equations, coupled by linear time-varying boundary conditions. The sufficient conditions is in terms of dissipativity of the couplings, which is…
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 this paper the unconditional stability of four well-known ADI schemes is analyzed in the application to time-dependent multidimensional diffusion equations with mixed derivative terms. Necessary and sufficient conditions on the parameter…
We provide convex necessary and sufficient conditions for the robust stability of linear positively dominated systems. In particular we show that the structured singular value is always equal to its convex upper bound for nonnegative…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
Many physical systems are inherently time-varying in nature. When these systems are linearized around a trajectory, generally, the resulting system is Linear Time-Varying (LTV). LTV systems describe an important class of linear systems and…
The stability of nonlinear explicit difference schemes with not, in general, open domains of the scheme operators are studied. For the case of path-connected, bounded, and Lipschitz domains, we establish the notion that a multi-level…
The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…
This paper studies cone-preserving linear discrete-time switched systems whose switching is governed by an automaton. For this general system class, we present performance analysis conditions for a broadly usable performance measure. In…
The stability analysis of synchronization patterns on generalized network structures is of immense importance nowadays. In this article, we scrutinize the stability of intralayer synchronous state in temporal multilayer hypernetworks, where…
Relationship for dynamical properties in the vicinity of fixed points between two-dimensional continuous and its positivity-preserving discretized dynamical systems is studied. Based on linear stability analysis, we reveal the conditions…
The linear switching system is a system of ODE with the time-dependent matrix taking values from a given control matrix set. The system is (asymptotically) stable if all its trajectories tend to zero for every control function. We consider…
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…
Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is,…
Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When…
In adaptive dynamical networks, the dynamics of the nodes and the edges influence each other. We show that we can treat such systems as a closed feedback loop between edge and node dynamics. Using recent advances on the stability of…
In this paper, we introduce the class of diagonally dominant (with respect to a given LMI region ${\mathfrak D} \subset {\mathbb C}$) matrices that possesses the analogues of well-known properties of (classical) diagonally dominant…