The paper presents the comparison of fuzzy conclusions derived from the use of t-norms with the fuzzy conclusions derived from the use of H-norm. The idea was to examine the application of H-logical norm to fuzzy reasoning, which is not monotonious while it is known that t-norms used in fuzzy reasoning have the characteristic of monotonicity. The comparison of fuzzy conclusions was performed by...

We consider delay differential algebraic equations (DDAEs) to model interconnected systems with time-delays. The DDAE framework does not require any elimination techniques and can directly deal with any interconnection of systems and controllers with timedelays. In this framework, we analyze the properties of the H-infinity norm of interconnected systems with time-delays. We show that the stand...

This paper focuses on the empirical autocovariance operator of H-valued periodically correlated processes. It will be demonstrated that the empirical estimator converges to a limit with the same periodicity as the main process. Moreover, the rate of convergence of the empirical autocovariance operator in Hilbert-Schmidt norm is derived.

This article studies the least-squares finite element method for the linearized, stationary Navier–Stokes equation based on the stress-velocity-pressure formulation in d dimensions (d = 2 or 3). The least-squares functional is simply defined as the sum of the squares of the L2 norm of the residuals. It is shown that the homogeneous least-squares functional is elliptic and continuous in the H(di...

We design fixed-order strong H-infinity controllers for general time-delay systems. The designer chooses the controller order and may introduce constant time-delays in the controller. We represent the closed-loop system of the plant and the controller as delay differential algebraic equations (DDAEs). This representation deals with any interconnection of systems with time -delays without any el...

Let S be a discrete semigroup, m (S) the space of all bounded real functions on S with the usualsupremum norm. Let Acm (S) be a uniformly closed left invariant subalgebra of m (S) with 1 c A. We say that A is extremely left amenable if there isamultiplicative left invariant meanon A. Let P = {h ?A: h =|g-1,g | forsome g ?A, s ?S}. It isshown that . A is extremely left amenable if and only ...

We find an expression for the Gateaux derivative of C⁎-algebra norm. Using this, we obtain a characterization orthogonality operator A∈B(H,K) to subspace, under assumption dist(A,K(H,K))<‖A‖. subdifferential set norm function at A∈B(H) when dist(A,K(H))<‖A‖. also give new proofs known results on closely related notions smooth points and Birkhoff-James spaces B(H) Cb(Ω), respectively.

this paper presents h∞ control problem for input-delayed systems. a neutral system approach is considered to the design of pd controller for input delay systems in presence of uncertain time-invariant delay. using this approach, the resulting closed-loop system turns into a specific time-delay system of neutral type. the significant specification of this neutral system is that its delayed coeff...

In a paper [1] the authors ask whether the Frobenius and the H norms are induced. There they claimed that the Frobenius norm is not induced, and consequently conjectured that the H-norm may not be induced. In this note it is shown that the Frobenius norm is induced on particular matrix spaces. It is then shown that the H-norm is in fact induced on a particular matrix-valued L1 space. NOTATION R...