Related papers: Lyapunov Criterion for Stochastic Systems and Its …
Here, we study the ultimately bounded stability of network of mismatched systems using Lyapunov direct method. We derive an upper bound on the norm of the error of network states from its average states, which it achieves in finite time.…
For a product of i.i.d. random maps or a memoryless stochastic flow on a compact space $X$, we find conditions under which the presence of locally asymptotically stable trajectories (e.g. as given by negative Lyapunov exponents) implies…
The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle…
We investigate the behavior of the Lyapunov spectrum of a linear discrete-time system under the action of small perturbations in order to obtain some verifiable conditions for stability and openness of the Lyapunov spectrum. To this end we…
We consider stability analysis of constrained switching linear systems in which the dynamics is unknown and whose switching signal is constrained by an automaton. We propose a data-driven Lyapunov framework for providing probabilistic…
We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in…
In this paper we consider the problem of minimizing a quadratic functional for a discrete-time linear stochastic system with multiplicative noise, on a standard probability space, in infinite time horizon. We show that the necessary and…
In chaotic dynamical systems such as the weather, prediction errors grow faster in some situations than in others. Real-time knowledge about the error growth could enable strategies to adjust the modelling and forecasting infrastructure…
We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by…
This paper studies the synchronization of stochastic linear systems which are subject to a general class of noises, in the sense that the noises are bounded in covariance but might be correlated with the states of agents and among each…
This paper considers a sampling-based approach to stability verification for piecewise continuous nonlinear systems via Lyapunov functions. Depending on the system dynamics, the candidate Lyapunov function and the set of initial states of…
The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response…
In this paper we provide a set of stability conditions for linear time-invariant networked control systems with arbitrary topology, using a Lyapunov direct approach. We then use these stability conditions to provide a novel low-complexity…
This paper establishes an existence theory for distributed periodic solutions to Newton's equation with stochastic time-periodic forcing, where the friction matrix is the Hessian of a twice continuously differentiable friction function.…
The robust tracking and model following problem of linear discrete-time systems is investigated in this paper. An approach to design robust tracking controllers is proposed. The system is controlled to track dynamic inputs generated from a…
We develop a powerful and general method to provide rigorous and accurate upper and lower bounds for Lyapunov exponents of stochastic flows. Our approach is based on computer-assisted tools, the adjoint method and established results on the…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
Stability and safety are crucial in safety-critical control of dynamical systems. The reach-avoid-stay objectives for deterministic dynamical systems can be effectively handled by formal methods as well as Lyapunov methods with soundness…