The set of all bounded linear functional operations on a given vector spacej plays an important role in the consideration of linear functional operations. For the sake of greater definiteness it is desirable to know the form of such operations and a space determined thereby. This problem has been solved for a number of spaces, for instance, all continuous functions on a bounded closed interval,...

This paper reveals the analytical structure of a fuzzy twoterm (PI/PD) controller which employs N1 (≥3) number of symmetric fuzzy sets for the input variable ‘displacement’, N2 (≥3) number of symmetric fuzzy sets for the input variable ‘velocity’ and N1+N2-1 number of symmetric fuzzy sets for the output variable ‘controller output’. The analytical structures are derived via triangular membershi...

1. An isomorphism theorem. In this paper we discuss a particular method of introducing a convolution product into certain topological linear spaces so that they become algebras. The space in each case will be essentially the dual space of a linear space of continuous functions, and arises in the study of general group algebras and in the theory of distributions. Let G be a topological group, wr...

This paper studies quantized and delayed state-feedback control of linear systems. We consider two types of quantization: quantized feedback and quantized state. The quantizer may be either unconstrained or saturated with a given quantization error bound. The delay is supposed to be time-varying and bounded. The controller is designed with the following property: all the states of the closed-lo...

This article presents a fuzzy sliding-mode control scheme for a class of Takagi-Sugeno (T-S) fuzzy which are subject to norm-bounded uncertainties in each subsystem. The proposed stabilization method can be adopted to explore T-S uncertain fuzzy systems (TSUFS) with various local control inputs. Firstly, a new design is proposed to transform TSUFS into sliding-mode dynamic systems.In addi...

in this paper, we introduce the concepts of norm and inner prod- uct on fuzzy linear spaces over fuzzy elds and discuss some fundamental properties.

In this manuscript, we introduce  a new class of fuzzy problems, namely ``fuzzy inclusion linear systems" and   propose a fuzzy solution set for it. Then, we present a theoretical discussion about the relationship between  the fuzzy solution set of a  fuzzy inclusion linear system and the algebraic solution of a fuzzy linear system. New necessary and sufficient conditions are derived for obtain...