Related papers: On the Diagonal Stability of $k$-Positive Linear S…
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…
This paper addresses the stability problem for discrete-time switched systems under autonomous switching. Each mode of the switched system is modeled as a Linear Parameter Varying (LPV) system, the time-varying parameters can vary…
In this note, a novel methodology that can extract a number of analysis results for linear time-invariant systems (LTI) given only a single trajectory of the considered system is proposed. The superiority of the proposed technique relies on…
A system is called positive if the set of non-negative states is left invariant by the dynamics. Stability analysis and controller optimization are greatly simplified for such systems. For example, linear Lyapunov functions and storage…
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…
A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of…
In this paper we study connections between structured storage or Lyapunov functions of a class of interconnected systems (dynamical networks) and dissipativity properties of the individual systems. We prove that if a dynamical network,…
A central question in verification is characterizing when a system has invariants of a certain form, and then synthesizing them. We say a system has a $k$ linear invariant, $k$-LI in short, if it has a conjunction of $k$ linear (non-strict)…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
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…
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 we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to external disturbances. We first extend the well-known Datko lemma to the framework of the considered class of systems. Thanks…
We consider non-i.i.d. random holomorphic dynamical systems whose choice of maps depends on Markovian rules. We show that generically, such a system is mean stable or chaotic with full Julia set. If a system is mean stable, then the…
This paper investigates the mean stability of a class of discrete-time stochastic switched linear systems using the $L^p$-norm joint spectral radius of the probability distributions governing the switched systems. First we prove a converse…
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…
Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…
We consider a class of matrices with a specific structure that arises, among other examples, in dynamic models for biological regulation of enzyme synthesis (Tyson and Othmer, 1978). We first show that a stability condition given in (Tyson…
In this paper, we consider the systems with trajectories originating in the nonnegative orthant becoming nonnegative after some finite time transient. First we consider dynamical systems (i.e., fully observable systems with no inputs),…
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…
We consider a simple model for multidimensional cone-wise linear dynamics around cusp-like equilibria. We assume that the local linear evolution is either $\mathbf{v}^\prime=\mathbb{A}\mathbf{v}$ or $\mathbb{B}\mathbf{v}$ (with…