We provide a formula for a stabilizing feedback law using a bounded control, under the assumption that an appropriate control-Lyapunov function is known. Such a feedback, smooth away from the origin and continuous everywhere, is known to exist via Artstein’s Theorem. As in the unbounded-control case treated in a previous note, we provide an explicit and “universal” formula given by an algebraic...

Products of random matrices associated to one-dimensional random media satisfy a central limit theorem assuring convergence to a gaussian centered at the Lyapunov exponent. The hypothesis of single parameter scaling states that its variance is equal to the Lyapunov exponent. We settle discussions about its validity for a wide class of models by proving that, away from anomalies, single paramete...

A class of virus dynamics model with intracellular delay and nonlinear infection rate of Beddington-DeAngelis functional response is analysed in this paper. By constructing suitable Lyapunov functionals and using LaSalle type theorem for delay differential equations, we show that the global stability of the infection-free equilibrium and the infected equilibrium depends on the basic reproductiv...

Abstract: This paper is concerned with the robust stability of a class of uncertain discrete-time systems with timevarying delays and state saturation nonlinearities. The saturation nonlinearities are assumed to be the standard saturation function, and the delay is allowed to be time-varying with known bounds. By applying the Lyapunov stability theorem and the delay-fractioning approach, a suit...

Asymptotic stability of finite-dimensional linear continuous-time periodic (FDLCP) systems is studied by the harmonic analysis. It is first shown that stability can be examined with what we call the harmonic Lyapunov equation. Another necessary and sufficient stability criterion is developed via this generalized Lyapunov equation, which reduces the stability test into that of an approximate FDL...

This paper investigates the mean stability of a class of discrete-time stochastic switched linear systems using the Lp-norm joint spectral radius of the probability distributions governing the switched systems. First we prove a converse Lyapunov theorem that shows the equivalence between the mean stability and the existence of a homogeneous Lyapunov function. Then we show that, when p goes to ∞...

This paper presents the relaxed nonquadratic stabilization conditions of discrete-time Takagi–Sugeno (T–S) fuzzy systems. To do this, we propose a new fuzzy controller and Lyapunov function by generalizing the nonparallel distributed compensation (non-PDC) control law and nonquadratic Lyapunov function, respectively. By exploiting Pólya’s theorem and algebraic properties of a homogeneous polyno...

This paper considers the robust stability problem for state space models via homogeneous polynomially parameter-dependent Lyapunov functions. The suggested approach is based on a quadratic in the vector of parametric monomials matrix representation of the time derivative of the Lyapunov function. At each step, sufficiency is provided by a set of relaxed linear matrix inequalities and check for ...

Physical systems, composed of interacting identical (or similar) subsystems appear in many branches of physics. They are standard in condensed matter physics. Assuming that each subsystem only interacts with its nearest neighbours and that the energy per subsystem has an upper limit, which must not depend on the number of subsystems n, we show that the distribution of energy eigenvalues of almo...

When robots are driven by the negative gradient of a potential field that consists of the sum of an attractive and a repulsive term, convergence to the desired configuration cannot be guaranteed by traditional Lyapunov techniques. In this paper, sufficient conditions for convergence of such systems are provided instead with the use of Rantzer’s Dual Lyapunov Theorem. In particular, a condition ...