Related papers: Global Stability of Dynamic Systems of High Order
In this paper, we'll show the robustness of global stability for perturbed dissipative dynamical systems.
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…
Stability is a critical feature of distributed linear multi-input-multi-output systems. Global asymptotic stability usually can be guaranteed when using decentralised or distributed control architectures, if: (i) conservative controllers…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
We prove conditions for global nonlinear stability of Oldroyd-B viscoelatic fluid flows in the Couette shear flow geometry. Global stability is inferred by analysing a new functional, called a perturbation entropy, to quantify the magnitude…
In the present work, sufficient conditions for global stabilization of nonlinear uncertain systems by means of discrete-delay static output feedback are presented. Illustrating examples show the efficiency of the proposed control strategy.
We study deterministic continuous-time lossy dynamical flow networks with constant exogenous demands, fixed routing, and finite flow and buffer capacities. In the considered model, when the total net flow in a cell ---consisting of the…
We present stability and recurrence results for a class of stochastic hybrid dynamical systems with oscillating flow maps. These results are developed by introducing averaging tools that parallel those already existing for ordinary…
We consider a dissipative vector field which is represented by a nearly-integrable Hamiltonian flow to which a non symplectic force is added, so that the phase space volume is not preserved. The vector field depends upon two parameters,…
This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control,…
This work considers a system coupling a viscous Burgers equation (aimed to describe a simplified model of $1D$ fluid flow) with the ODE describing the motion of a point mass moving inside the fluid. The point mass is possibly under the…
This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative…
Verifying nonlinear stability of a laminar fluid flow against all perturbations is a central challenge in fluid dynamics. Past results rely on monotonic decrease of a perturbation energy or a similar quadratic generalized energy. None show…
This paper is concerned with establishing global asymptotic stability results for a class of non-linear PDE which have some similarity to the PDE of the Lifschitz-Slyozov-Wagner model. The method of proof does not involve a Lyapounov…
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
Suppose that two vector fields on a smooth manifold render some equilibrium point globally asymptotically stable (GAS). We show that there exists a homotopy between the corresponding semiflows such that this point remains GAS along this…
The asymptotic stability of a global solution satisfying Hamilton-Jacobi equations with jumps will be analyzed in dependence on the strong dissipativity of the jump control function and using orbits of the differentiable flows to describe…
We develop a method to prove almost global stability of stochastic differential equations in the sense that almost every initial point (with respect to the Lebesgue measure) is asymptotically attracted to the origin with unit probability.…
We review works on the asymptotic stability of the Couette flow. The majority of the paper is aimed towards a wide range of applied mathematicians with an additional section aimed towards experts in the mathematical analysis of PDEs.
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…