Abstract In this paper, we present that the propositional proof system R(lin) (Resolution over Linear Equations) established by Ran Raz and Iddo Tzameret is not a super system, there exists a sequence of tautologies, which require proof complexity exponential in size of tautologies. We show that there are the sequence of unsatisfiable collections of disjuncts of linear equations, which require ...

This paper deals with resilient robust H∞ fuzzy control problem for a class of nonlinear time-delayed systems with norm-bounded and time-varying uncertainties in the matrices of state, delayed state and control gain via state feedback controllers. Firstly, the nonlinear system is represented by Takagi-Sugeno (TS) fuzzy model. Sufficient conditions are derived for the existence of resilient robu...

Theorems on the Fredholm alternative and well-posedness of the linear boundary value problem u′(t)= (u)(t) + q(t), h(u)= c, where : C([a,b];R)→ L([a,b];R) and h : C([a, b];R)→ R are linear bounded operators, q ∈ L([a,b];R), and c ∈ R, are established even in the case when is not a strongly bounded operator. The question on the dimension of the solution space of the homogeneous equation u′(t)= (...

These informal notes deal with some very basic objects in functional analysis, including norms and seminorms on vector spaces, bounded linear operators, and dual spaces of bounded linear functionals in particular.

This paper studies the problem of dynamic output feedback H∞ control for nonlinear systems, which are described by Takagi–Sugeno fuzzy parts with measurable premise variables and uncertainty parts. The uncertainties are parameter dependent, unknown, and time varying but bounded. A switching fuzzy dynamic output feedback control scheme is proposed, which depends on the measurable premise variabl...

Abstract. The question about the existence and characterization of bounded solutions to linear functional-differential equations with both advanced and delayed arguments was posed in early 1970s by T. Kato in connection with the analysis of the pantograph equation, y(x) = ay(qx) + by(x). In the present paper, we answer this question for the balanced generalized pantograph equation of the form −...

In this work, we give a new variation of constants formula for some partial functional differential equations with infinite delay. We assume that the linear part is not necessarily densely defined and satisfies the known Hille-Yosida condition. When the phase space is a uniform fading memory space, we establish a spectral decomposition of the phase space. This allows us to study the existence o...

A fuzzy regression model is used in evaluating the functional relationship between the dependent and independent variables in a fuzzy environment. Most fuzzy regression models are considered to be fuzzy outputs and parameters but non-fuzzy (crisp) inputs. In general, there are two approaches in the analysis of fuzzy regression models: linear-programmingbased methods and fuzzy least-squares meth...

To date, nonlinearL∞-gain control problems have not been solved by the conventional control methods for the nonlinear dynamic systems with persistent bounded disturbances. This study introduces a fuzzy control design to deal with the nonlinear L∞-gain output feedback control problem. First, the Takagi and Sugeno (T–S) fuzzymodel is employed to approximate the nonlinear dynamic system. Next, bas...