Related papers: Stability analysis and optimal control of the logi…
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 provides sufficient conditions for global asymptotic stability and global exponential stability, which can be applied to nonlinear, large-scale, uncertain discrete-time systems. The conditions are derived by means of vector…
This brief gives a set of unified Lyapunov stability conditions to guarantee the predefined-time/finite-time stability of a dynamical systems. The derived Lyapunov theorem for autonomous systems establishes equivalence with existing…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
This paper studies finite-time stability and instability theorems in probability sense for stochastic nonlinear systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global solution.…
In this paper quotients of control systems which are generalizations of system reductions are used to study the stabilizability property of non-linear systems. Given a control system and its quotient we study under what conditions…
We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular…
We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…
In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…
The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…
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…
Solutions of a smooth first order dynamic equation can be made Lyapunov stable at will by the choice of an appropriate time-dependent Riemannian metric.
Using the formalism of Lyapunov potential function it is shown that the stability principles for biomass in the ecosystem and for employment in economics are mathematically similar. The ecosystem is found to have a stable and an unstable…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
We use Lyapunov-like functions and convex optimization to propagate uncertainty in the initial condition of nonlinear systems governed by ordinary differential equations. We consider the full nonlinear dynamics without approximation,…
We study the stability of circular orbits in the background of a traversable wormhole (TWH) spacetime obtained as a solution of Einstein's field equations coupled conformally to a massless scalar field. The Lyapunov stability approach is…
This paper deals with the stability analysis of a mass-spring system subject to friction using Lyapunov-based arguments. As the described system presents a stick-slip phenomenon, the mass may then periodically sticks to the ground. The…