In this paper we present two approaches to estimate the Hausdorff dimension of an invariant compact set of a dynamical system: the method of characteristic exponents (estimates of KaplanYorke type) and the method of Lyapunov functions. In the first approach, using Lyapunov's first method we exploit charachteristic exponents for obtaining such estimate. A close relationship with uniform asymptot...

We prove optimality principles for semicontinuous bounded viscosity solutions of HamiltonJacobi-Bellman equations. In particular we provide a representation formula for viscosity supersolutions as value functions of suitable obstacle control problems. This result is applied to extend the Lyapunov direct method for stability to controlled Ito stochastic differential equations. We define the appr...

In this paper, we use what we call the shift operator so that general delay dynamic equations of the form x∆(t) = a(t)x(t)+b(t)x(δ−(h,t))δ−(h,t), t ∈ [t0,∞)∩T can be analyzed with respect to stability and existence of solutions. By means of the shift operators, we define a general delay function opening an avenue for the construction of Lyapunov functional on time scales. Thus, we use the Lyapu...

A new position controller with gravity compensation for robot manipulators in joint space is proposed in this paper. The goal of position control problem for global asymptotically stability is achieved by using Lyapunov ’s direct method and LaSalle ’s invariance principle over the full non—linear mutivariable robot closed—loop system. In adition, this paper also presents experimental results on...

*Correspondence: [email protected] School of Mathematical Science, Anhui University, Hefei, P.R. China Abstract In this paper, using the theory of q-fractional calculus, we deal with the q-Mittag-Leffler stability of q-fractional differential systems, and based on it, we analyze the direct Lyapunov method of q-fractional differential systems. Several sufficient criteria are established to guaran...

Conditions for robust stability in linear continuous systems are derived, when all matrices of the state-space model are perturbed by independent uncertain parameters and static output feedback is applied. Two diierent approaches are presented. Then, improved conditions for robust stability in linear discrete-time systems with both un-structured and structured perturbations in the system matrix...

This study addresses the adaptive synchronization of Rössler and Chua circuit systems with unknown parameters. By using Lyapunov stability theory the adaptive synchronization law with a single-state variable feedback is derived, such that the trajectory of the two systems are globally stabilized to an equilibrium point of the uncontrolled system (globally stable means that the method of the sol...

In this work we deal with global stability properties of classic SIS, SIR and SIRS epidemic models with constant recruitment rate, mass action incidence and variable population size. The usual approach to determine global stability of equilibria is the direct Lyapunov method which requires the construction of a function with specific properties. In this work we construct different Lyapunov func...

In this paper, a novel adaptive visual feedback scheme is presented to solve the problem of controlling the relative pose between a robot camera and a rigid object of interest. By exploiting nonlinear controllability properties, uniform asymptotic stability in the large of the image reference set-point is proved using Lyapunov’s direct method. Moreover, uniform boundedness of the whole state ve...