In this paper, we describe an algorithm for estimating the H∞-norm of a large linear time invariant dynamical system described by a discrete time state-space model. The algorithm is designed to be efficient for state-space models defined by {A, B,C, D} where A is a large sparse matrix of order n which is assumed very large relative to the input and output dimensions of the system.

Abstract. We study the H-norm of the function 1 on tubular neighbourhoods of curves in R. We take the limit of small thickness ε, and we prove two different asymptotic results. The first is an asymptotic development for a fixed curve in the limit ε → 0, containing contributions from the length of the curve (at order ε), the ends (ε), and the curvature (ε). The second result is a Γ-convergence r...

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The problem of estimating the state vector of a dynamical system from vector measurements when it is known that the state vector satisfies norm equality constraints is considered. The case of a linear dynamical system with linear measurements subject to a norm equality constraint is discussed with a review of existing solutions. The norm constraint introduces a nonlinearity in the system for wh...

Let's consider the stochastic differential equation \[\left\{ \begin{split} dX_t&=\sigma(X_t,V_t )dW_t+b(X_t,R_t)dt\\ X_0&=x>0 \end{split}\right. \] In this paper, we establish support theorem for positive random evolution type on $C^{\alpha,0}([0;1];\mathbb{R})$. We use linear interpolations of $W$ proof.

We define the discrete norm of a complex m× n matrix A by ‖A‖∆ := max 06=ξ∈{0,1}n ‖Aξ‖ ‖ξ‖ , and show that c √ log h(A) + 1 ‖A‖ ≤ ‖A‖∆ ≤ ‖A‖, where c > 0 is an explicitly indicated absolute constant, h(A) = √ ‖A‖1‖A‖∞/‖A‖, and ‖A‖1, ‖A‖∞, and ‖A‖ = ‖A‖2 are the induced operator norms of A. Similarly, for the discrete Rayleigh norm ‖A‖P := max 06=ξ∈{0,1} 06=η∈{0,1} |ξAη| ‖ξ‖‖η‖ we prove the esti...

The problem of nding bounds on the H∞-norm of systems with a nite number of point delays and distributed delay is considered. Su cient conditions for the system to possess an H∞-norm which is less or equal to a prescribed bound are obtained in terms of Riccati partial di erential equations (RPDE’s). We show that the existence of a solution to the RPDE’s is equivalent to the existence of a stabl...

This paper develops a least-squares approach to the solution of the incompressible Navier–Stokes equations in primitive variables. As with our earlier work on Stokes equations, we recast the Navier–Stokes equations as a first-order system by introducing a velocity-flux variable and associated curl and trace equations. We show that a least-squares principle based on L norms applied to this syste...