In this paper the problem of robust control for a class of linear infinite dimensional systems under mixed disturbances of the multiplicative type is addressed. The Lyapunov function approach is used for proving that there is a controller that stabilizes this class of systems under the presence of uncertainties and perturbations, and guarantees some tolerance level for the joint cost functional...

The work examines the problem of model predictive control for uncertain linear dynamic systems with intervally assigned parameters and multiplicative noise inputs. We use the model predictive control techniques based on linear matrix inequalities to get an optimal robust control strategy that provides the system with stability in the mean-square sense. The results are illustrated by an numerica...

‎hensel [k‎. ‎hensel‎, ‎deutsch‎. ‎math‎. ‎verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎then $|x...

This paper focuses on certain finite dimensional point derivations for the non-selfadjoint operator algebras corresponding to directed graphs. We begin by analyzing the derivations corresponding to full matrix representations of the tensor algebra of a directed graph. We determine when such a derivation is inner, and describe situations that give rise to non-inner derivations. We also analyze t...

We consider a linear stochastic differential equation with drift and multiplicative noise. study the problem of approximating its solution process that solves where possibly is replaced by deterministic function. To do this, we use combination Pontryagin’s maximum principle approach direct methods calculus variations. find necessary sufficient conditions for function $$u \in L^1(0, T)$$ to be m...

We present the logic of bunched implications, BI, in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication, and may be viewed as a merging of intuitionistic logic and multiplicative, intuitionistic linear logic. The predi...

We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication; it can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen cate...

In this paper, we study sufficient conditions for the emergence of asymptotic consensus and flocking in a certain class non-linear generalised Cucker-Smale systems subject to multiplicative communication failures. Our approach is based on combination strict Lyapunov design together with formulation suitable persistence condition multi-agent systems. The latter can be interpreted as lower bound ...

This paper discusses the instability of eleven nonlinear state space models that underly exponential smoothing. Hyndman et al. (2002) proposed a framework of 24 state space models for exponential smoothing, including the well-known simple exponential smoothing, Holt’s linear and Holt-Winters’ additive and multiplicative methods. This was extended to 30 models with Taylor’s (2003) damped multipl...