Related papers: An Input-to-State Stability Perspective on Robust …
Achieving highly dynamic behaviors on humanoid robots, such as running, requires controllers that are both robust and precise, and hence difficult to design. Classical control methods offer valuable insight into how such systems can…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
Recurrent neural network-based reinforcement learning systems are capable of complex motor control tasks such as locomotion and manipulation, however, much of their underlying mechanisms still remain difficult to interpret. Our aim is to…
The Degasperis-Procesi (DP) equation is an integrable Camassa-Holm-type model as an asymptotic approximation for the unidirectional propagation of shallow water waves. This work is to establish the $L^2\cap L^\infty$ orbital stability of a…
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 proposes several Converse Lyapunov Theorems for nonlinear dynamical systems defined on smooth connected Riemannian manifolds and characterizes properties of corresponding Lyapunov functions in a normal neighborhood of an…
Incremental stability is a property of dynamical and control systems, requiring the uniform asymptotic stability of every trajectory, rather than that of an equilibrium point or a particular time-varying trajectory. Similarly to stability,…
For the deployment of legged robots in real-world environments, it is essential to develop robust locomotion control methods for challenging terrains that may exhibit unexpected deformability and irregularity. In this paper, we explore the…
Most of nonlinear robust control methods just consider the affine nonlinear nominal model. When the nominal model is assumed to be affine nonlinear, available information about existing non-affine nonlinearities is ignored. For non-affine…
Nonlinear robust control is pursued by overcoming the drawback of linear robust control that it ignores available information about existing nonlinearities and the resulting controllers may be too conservative, especially when the…
Incremental stability is a property of dynamical systems that ensures the convergence of trajectories with respect to each other rather than a fixed equilibrium point or a fixed trajectory. In this paper, we introduce a related stability…
The present paper is mainly aimed at introducing a novel notion of stability of nonlinear time-delay systems called Rational Stability. According to the Lyapunov-type, various sufficient conditions for rational stability are reached. Under…
The paper endeavours to solve the problem of the necessary and sufficient conditions for testing asymptotic stability of the equilibrium state without using a positive definite or semi-definite Lyapunov function for time-invariant nonlinear…
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…
A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable to disrupt the system and switch it…
?In this work, we study the orbital stability of stationary solutions to the relativistic Vlasov-Manev system. This system is a kinetic model describing the evolution of a stellar system subject to its own gravity with some relativistic…
Unlike ordinary differential equations (ODEs), linear partial differential equations (PDEs) admit multiple non-equivalent notions of stability. This variety makes interpretation of Lyapunov stability results challenging. \blue{To simplify…
This paper deals with existence and robust stability of hybrid limit cycles for a class of hybrid systems given by the combination of continuous dynamics on a flow set and discrete dynamics on a jump set. For this purpose, the notion of…
A safety-critical measure of legged locomotion performance is a robot's ability to track its desired time-varying position trajectory in an environment, which is herein termed as "global-position tracking". This paper introduces a nonlinear…
In this paper, we study the Poisson stability (in particular, stationarity, periodicity, quasi-periodicity, Bohr almost periodicity, almost automorphy, recurrence in the sense of Birkhoff, Levitan almost periodicity, pseudo periodicity,…