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 uses Chandrasekhar iterations to obtain an estimate of theH∞-norm and then uses extrapolation to improve these estimates. Résumé. Nous décrivons un algorithme pour estimer la norme H∞ d’un système dynamique linéaire à temps invariant...

This paper considers a hybrid evolutionaryalgebraic approach to the non-convex problem of designing low-order H∞ optimal controllers. It is shown that using the closed-loop H∞ norm as fitness measure in a population-based, evolutionary search does not require the computation of the H∞ norm for each controller of the population. Instead, the fact that evolutionary algorithms assign fitness measu...

In this paper, firstly we introduce the concept of norm-to-weak continuous cocycle in Banach space and give a technical method to verify this kind of continuity, then we obtain some abstract results for the existence of pullback attractors about this kind of cocycle, using the measure of noncompactness. As an application, we prove the existence of pullback attractors in H 1 0 of the cocycle ass...

We define the complete numerical radius norm for homomorphisms from any operator algebra into B(H), and show that this norm can be computed explicitly in terms of the completely bounded norm. This is used to show that if K is a complete Cspectral set for an operator T , then it is a complete M -numerical radius set, where M = 12 (C + C −1). In particular, in view of Crouzeix’s theorem, there is...

The paper examines the stabilization and the H∞ norm performance analysis and control of state-delayed systems with a symmetric state-space realization. Such symmetric realizations appear in many engineering applications. By exploiting the state-space symmetry, we obtain an explicit solution for a bound on the H∞ norm of such symmetric time-delayed systems. Also, we derive an explicit parametri...

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 uses Chandrasekhar iterations to obtain an estimate of theH∞-norm and then uses extrapolation to improve these estimates. Résumé. Nous décrivons un algorithme pour estimer la norme H∞ d’un système dynamique linéaire à temps invariant...

We discuss solvability issues of H−/H2/∞ optimal fault detection problems in the most general setting. A solution approach is presented which successively reduces the initial problem to simpler ones. The last computational step generally may involve the solution of a non-standardH−/H2/∞ optimization problem for which we discuss possible solution approaches. Using an appropriate definition of th...

In this paper we discuss a multi-objective control problem that involves several H 2-norm and H 1-norm constraints. In an accompanying paper we show how to eeciently compute a sequence of upper bounds that converges monotonically from above to the optimal value of such problems. If more than one H 1 constraint is involved, it is so far unknown and revealed in this paper how to compute as well a...

We develop and analyze a first-order system least-squares spectral method for the second-order elliptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the Lwand H−1 w norm of the residual equations and then we replace the negative norm by the discrete negative norm and analyze the discrete Chebyshev ...

Optimal finite impulse response (FIR) error feedback filters for noise shaping in modulators are designed by using weighting functions based on the system norms. We minimize the weighted norms of the quantization error in the output of a modulator, which corresponds to the minimization of the system norm. Three norms, the H2 system norm, the H∞ system norm, and the l1 norm of the impulse respon...