In this paper, we propose fixed-order set-valued (in the form of l2-norm hyperballs) observers for some classes nonlinear bounded-error dynamical systems with unknown input signals that simultaneously find bounded hyperballs states and inputs include true inputs. Necessary sufficient conditions in Linear Matrix Inequalities (LMIs) stability sense quadratic stability) proposed are derived ($\mat...

in this paper we study the almost universal convergence of weighted sums for sequence {x ,n } of negatively dependent (nd) uniformly bounded random variables, where a, k21 is an may of nonnegative real numbers such that 0(k ) for every ?> 0 and e|x | f | =0 , f = ?(x ,…, x ) for every n>l.

In this paper, the disturbance attenuation properties in the sense of uniformly ultimate boundedness are investigated for a class of switched linear systems with parametric uncertainties and exterior disturbances. The aim is to characterize the conditions under which the switched system can achieve a finite disturbance attenuation level. First, arbitrary switching signals are considered, and a ...

In recent times, a variety of reinforcement learning (RL) algorithms have been proposed for optimal tracking problem continuous time nonlinear systems with input constraints. Most these are based on the notion uniform ultimate boundedness (UUB) stability, in which normally higher rates avoided order to restrict oscillations state error smaller values. However, this comes at cost convergence cri...

Many crystalline materials exhibit solid-to-solid martensitic phase transformations in response to certain changes in temperature or applied load. These martensitic transformations result from a change in the stability of the material’s crystal structure. It is, therefore, desirable to have a detailed understanding of the possible modes through which a crystal structure may become unstable. The...

We study the dynamics of generic unfoldings of saddle-node circle local diffeomorphisms from the measure theoretical point of view, obtaining statistical stability results for deterministic and random perturbations in these kind of one-parameter families. In particular we show that the map is uniformly expanding for all parameters close enough to the parameter of the saddle-node and have positi...

Let  $left{a_alpharight}_{alphain I}$ be a bounded net in a Banach algebra $A$ and $varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $|aa_alpha-varphi(a)a_alpha|to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such  as Segal algebras and $L^1$-algebras are resp...

This paper develops an adaptive fixed-time trajectory tracking controller of underactuated hovercraft with a prescribed performance in the presence model uncertainties and unknown time-varying environment disturbances. It is first time that proposed method applied to motion control hovercraft. To begin with, based on hovercraft's four degrees freedom (DOF) model, virtual laws are designed using...

This paper addressed the formation control problem of surface unmanned vessels with model uncertainty, parameter perturbation, and unknown environmental disturbances. A method based on force saturation constraint extended state observer (ESO) was proposed. Compared methods which only consider disturbances from external environment, proposed in this took uncertainties, environment as compound di...

Suppose that f(z) is a transcendental entire function and that the Fatou set F (f) 6= ∅. Set B1(f) := sup U supz∈U log(|z| + 3) infw∈U log(|w|+ 3) and B2(f) := sup U supz∈U log log(|z|+ 30) infw∈U log(|w| + 3) , where the supremum supU is taken over all components of F (f). If B1(f) < ∞ or B2(f) < ∞, then we say F (f) is strongly uniformly bounded or uniformly bounded respectively. In this arti...