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The Langevin dynamics of a system exhibiting a Fluctuation Induced First Order Phase Transition is solved within the self consistent Hartree Approximation. Competition between interactions at short and long length scales gives rise to…
Propositional temporal logic over the real number time flow is finitely axiomatisable, but its first-order counterpart is not recursively axiomatisable. We study the logic that combines the propositional axiomatisation with the usual axioms…
We consider all pure or mixed states of a quantum many-body system which exhibit the same, arbitrary but fixed measurement outcome statistics for several commuting observables. Taking those states as initial conditions, which are then…
Recent works have revealed that matching conditions play a major role on general consistency properties of relativistic fluid dynamics such as causality, stability and wellposedness of the equations of motion. In this paper we derive…
Stability criteria are given for linear periodic Hamiltonian systems with impulse effect. A Lyapunov type inequality and a disconjugacy criterion are also established. The results improve the ones in the literature for such systems.
This paper deals with the stability analysis problem of discrete-time switched linear systems with ranged dwell time. A novel concept called L-switching-cycle is proposed, which contains sequences of multiple activation cycles satisfying…
Given a discrete-state continuous-time reactive system, like a digital circuit, the classical approach is to first model it as a state transition system and then prove its properties. Our contribution advocates a different approach: to…
It is difficult to analyze the stability of systems with time-varying delays. One approach is to construct a time-transformation that converts the system into a form with a constant delay but with a time-varying scalar appearing in the…
Solutions to the interval observation problem for delayed impulsive and switched systems with $L_1$-performance are provided. The approach is based on first obtaining stability and $L_1/\ell_1$-to-$L_1/\ell_1$ performance analysis…
Stability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of…
Multivariate fluctuation relations are established in three stochastic models of transistors, which are electronic devices with three ports and thus two coupled currents. In the first model, the transistor has no internal state variable and…
We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…
We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide…
The paper studies the relation between a nonlinear time-varying flat discrete-time system and the corresponding linear time-varying systems which are obtained by a linearization along trajectories. It is motivated by the continuous-time…
The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to…
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…
This paper investigates a well-posedness property of parametric constraint systems named here Robinson stability. Based on advanced tools of variational analysis and generalized differentiation, we derive first-order and second-order…
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…
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…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…