The paper investigates linear functionals ϕ : ℝn → ℝ preserving a set ℳ⊆ ℝ, i.e., such that ϕ(v) ∈ ℳ for any vector u with components in ℳ. For various types of subsets real numbers, characterizations the preserve them are obtained. In particular, sets ℤ,ℚ, ℤ+,ℚ+,ℝ+, several infinite integers, bounded and unbounded intervals, finite numbers considered. A characterization also allows one to desc...

In this paper, we give the factorizations of Lucas and inverse matrices. We also investigate Cholesky factorization symmetric matrix. Moreover, obtain upper lower bounds for eigenvalues matrix by using some majorization techniques.

the paper is concerned with robust stability criteria for takagi- sugeno (t-s) fuzzy systems with distributed delays and time delay in the leakage term. by exploiting a model transformation, the system is converted to one of the neutral delay system. global robust stability result is proposed by a new lyapunov-krasovskii functional which takes into account the range of delay and by making use o...

there are two significant goals in teleoperation systems: stability and performance. this paper introduces an lmi-based robust control method for bilateral transparent teleoperation systems in presence of model mismatch. the uncertainties in time delay in communication channel, task environment and model parameters of master-slave systems is called model mismatch. the time delay in communicatio...