We study a characteristic subgroup of finitely generated groups, consisting elements with uniform upper bound for word-lengths. For group $G$, we denote this by $G\\mathrm{bound}$. give sufficient criteria triviality and finiteness prove that if $G$ is virtually abelian then $G\\mathrm{bound}$ finite. In contrast numerous examples where trivial, show every finite $A$, there exists an infinite $...

This article addresses the tracking control problem for a class of nonlinear systems described by Euler–Lagrange equations with uncertain system parameters. The proposed scheme is capable guaranteeing prescribed performance from two aspects: 1) special parameter estimator prescribed-performance properties embedded in scheme. not only ensures exponential convergence estimation errors under relax...

This paper is devoted to studying a reaction-diffusion-chemotaxis model with a volume-filling effect in a bounded domain with Neumann boundary conditions. We first establish the global existence of classical solutions bounded uniformly in time. Then applying the asymptotic analysis and bifurcation theory, we obtain both the local and global structure of steady states bifurcating from the homoge...

A fault-tolerant control scheme with thruster redundancy is developed and applied to perform attitude tracking manoeuvres for an orbiting flexible spacecraft. Based on the assumption of bounded elastic vibrations, an adaptive sliding mode controller is proposed to guarantee that all the signals of the resulting closed-loop attitude system are uniformly ultimately bounded in the presence of an u...

This article is devoted to the fuzzy fault-tolerant tracking control of Markov jump systems with unknown mismatched faults. To reconstruct faults and system states, a sequence proportional–integral observers are established via outputs. With help structure separation technique, gains observer solved by unified linear matrix inequality framework. Resorting rebuilt states from an iterative estima...

We study the large-time behaviour of a non-local evolution equation for the density of particles or individuals subject to an external and an interaction potential. In particular, we consider interaction potentials which are singular in the sense that their first derivative is discontinuous at the origin. For locally attractive singular interaction potentials we prove under a linear stability c...

We consider the Nernst-Planck-Navier-Stokes system in a bounded domain of ${\mathbb {R}}^d$, $d=2,3$ with general nonequilibrium Dirichlet boundary conditions for ionic concentrations. prove existence smooth steady state solutions and present sufficient condition terms only data that guarantees these have nonzero fluid velocity. show time evolving are ultimately uniformly, independently their i...

This study presents a novel means of designing a simple and effective torque controller for Permanent Magnet Synchronous Motor (PMSM). The overall stability of the system is shown using Lyapunov technique. The Lyapunov functions used contain a term penalizing the integral of the tracking error, enhancing the stability. The tracking error is shown to be globally uniformly bounded. Simulation res...