We introduce an interpolation framework for H∞ model reduction founded on ideas originating in optimal-H2 interpolatory model reduction, realization theory, and complex Chebyshev approximation. By employing a Loewner “data-driven” framework within each optimization cycle, large-scale H∞ norm calculations can be completely avoided. Thus, we are able to formulate a method that remains effective i...

We show that, if A is a finite-dimensional *-simple associative algebra with involution (over the field K of real or complex numbers) whose hermitian part H( A, * > is of degree > 3 over its center, if B is a unital algebra with involution over 06, and if (I.11 is an algebra norm on H( A @ B, * 1, then there exists an algebra norm on A @ B whose restriction to H(A @ B, *> is equivalent to 11 . ...

Let D be a masa in B(H) where H is a separable Hilbert space. We find real numbers η0 < η1 < η2 < · · · < η6 so that for every bounded, normal D-bimodule map Φ on B(H), either ‖Φ‖ > η6 or ‖Φ‖ = ηk for some k ∈ {0, 1, 2, 3, 4, 5, 6}. When D is totally atomic, these maps are the idempotent Schur multipliers and we characterise those with norm ηk for 0 ≤ k ≤ 6. We also show that the Schur idempote...

We consider systems governed by partial differential equations with spatially periodic coefficients over unbounded domains. These spatially periodic systems are considered as perturbations of spatially invariant ones, and we develop perturbation methods to study their stability and H system norm. The operator Lyapunov equations characterizing the H norm are studied using a special frequency rep...

A generalized dynamical robust nonlinear filtering framework is established for a class of Lipschitz differential algebraic systems, in which the nonlinearities appear both in the state and measured output equations. The system is assumed to be affected by norm-bounded disturbance and to have both norm-bounded uncertainties in the realization matrices as well as nonlinear model uncertainties. W...

Anderson acceleration (AA) is a technique for accelerating the convergence of fixed-point iterations. In this paper, we apply AA to sequence functions and modify norm in its internal optimization problem H−s norm, some positive integer s, bias it towards low-frequency spectral content residual. We analyze by quantifying improvement over Picard iteration. find that based on H−2 well-suited solve...

Henceforth, it will be assumed that (1.1) has a unique solution U. Precise hypotheses on the required smoothness of the solution will be made when needed. For s a nonnegative integer, let H” = H”(Q) be the Sobolev space W,“(R) of real-valued functions on R and let 11. /Is denote its usual norm. Let fi’ = ii’(Q) = {u E H’ :ulm = 0). Th e inner product on L* = L’(Q) is denoted by (. , .) and the ...

We present a new scaleable algorithm for approximating the H∞ norm, an important robust stability measure for linear dynamical systems with input and output. Our spectral value set based method uses a novel hybrid expansion-contraction scheme that, under reasonable assumptions, is guaranteed to converge to a stationary point of the optimization problem defining the H∞ norm, and, in practice, ty...

An isolated electrical network with an independent local distributed generator is very sensitive towards the contingencies between load demand and supply. Although system has less complexity in term of structure, its stability condition crucial due to stand-alone operating condition. Hence, monitor network, total power deficit only variable that can be estimated. This study proposed utilize fil...