We show that existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided an additional mild assumption is fulfilled. For UGAS infinite-dimensional systems with external disturbances we derive a novel ’integral’ construction of non-coercive Lipschitz continuous Lyapunov functions. F...

Making use of the neural network universal approximation ability, a nonlinear predictive control scheme is studied in this paper. On the basis of a uniform structure of simple recurrent neural networks, a one-step neural predictive controller (OSNPC) is designed. The whole closed-loop system’s asymptotic stability and passivity are discussed, and stable conditions for the learning rate are dete...

Guaranteeing that traditional concepts of stability like uniform global exponential or asymptotic stability (UGES or UGAS) are veri ed when using design tools based on new concepts of stability may be of signi cant importance. It is especially so when attempting to bridge the gap between theory and practice. This paper addresses the question of the applicability of contraction theory to the des...

The problems of absolute stability and existence of forced oscillations for systems with sector restricted nonlinearities are considered. An overview of the results for systems described by ordinary differential equations with constant and periodic coefficients is presented. A result is obtained on exponential absolute stability for systems described by ordinary differential equations. Next, a ...

In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov's second method. The results obtained essentially improve, include and complement the results in the literature.

In this article, we survey the asymptotic stability analysis of fractional differential systems with the Prabhakar fractional derivatives. We present the stability regions for these types of fractional differential systems. A brief comparison with the stability aspects of fractional differential systems in the sense of Riemann-Liouville fractional derivatives is also given. 

In this work, the asymptotic behavior of solutions to a coupled hyperbolic/parabolic{like system is investigated. It is shown that with both components of the equation being subjected to nonlinear damping (boundary damping for the wave component, interior for the beam), a global uniform stability is attained for all (weak) solutions.