Davut Kavranoglu

Characterization of the solution to the optimal H∞ model reduction problem

Abstract In this paper the H ∞ norm approximation of a given stable, proper, rational transfer function by a lower order stable proper rational transfer function is studied. The solution method is based on the authors observation that the H ∞ model reduction problem can be converted into a Hankel norm model reduction problem. A simple characterization of the solution to the optimal H ∞ model reduction problem is developed.

Zeroth order H ∞ norm approximation of multivariable systems

In this paper the H ∞ norm approximation of a given stable, proper, rational transfer function by a constant matrix is considered (Zeroth order H ∞ norm approximation problem). The solution method is based on the observation that the H ∞ norm approximation problem can be put into an allpass imbedding problem.

H/sub /spl infin//-norm approximation of systems by constant matrices and related results

In this work the H/sub /spl infin//-norm approximation of a given stable proper rational transfer function by a constant matrix is considered. A new improved bound on H/sub /spl infin//-norm of a given stable transfer function is derived. Optimal approximation for relaxation systems is given. >

Characterization and computation of the solution to the optimal L/sub /spl infin// approximation problem

The characterization of the solution to the problem of approximating a given stable, proper, rational transfer function, in L/sub /spl infin// norm sense, by a rational function with prescribed number of stable and unstable modes is developed. A simple state-space suboptimal computational algorithm for the solution is presented. >

A computational scheme for H/spl infin/ model reduction

In this paper, a computational scheme for the H/spl infin/ model reduction problem is introduced. The scheme is illustrated by three examples. The algorithm is based on the recent characterization of the solution to the H/spl infin/ model reduction problem. A suboptimal computational procedure for the general multivariable continuous-time rth order optimal H/sub /spl infin// model reduction problem is developed. >

Direct state-space solution to the discrete-time H/sub infinity / one-block problem

A general state-space representation is used to allow a complete formulation of the H/sub infinity / optimization problem without any invertibility condition on the system matrix, unlike existing solutions. A straightforward approach is used to solve the one-block H/sub infinity / optimization problem. The parameterization of all solutions to the discrete-time H/sub infinity / suboptimal one-block problem is first given in transfer function form in terms of a set of functions in H/sub infinity / that satisfy a norm bound. The parameterization of all solutions is also given as a linear fractional representation. >

Optimal L/sub /spl infin// norm model approximation with prescribed pole locations

In this paper the problem of optimal L/sub /spl infin// norm approximation of a given transfer function (possibly unstable) by another transfer function with given pole locations is solved. The problem is reduced into an equivalent to convex optimization problem involving linear matrix inequalities, which can be readily solved using interior point methods.<<ETX>>

Rational L ∞ norm approximation of multivariable systems

The problem of rational L/sub /spl infin// norm approximation of multivariable systems is treated in this paper. L/sub /spl infin// norm approximation of simultaneous muitivariable systems by a rational matrix function with desired number of stable and unstable poles is obtained using LMI based formulation of the problem. Several LMI based iterative algorithms are proposed for the computation of the solution.

A new general state-space representation for discrete-time systems

Abstract A new general state-space representation for causal and anticausal discrete-time systems is introduced. Some of its properties related to systems and network theory concepts are developed. The relation to the descriptor form state-space representation is also explained. Applications are given to show the usefulness of the new representation.

LMI Based Computational Schemes for H∞ Model Reduction

Abstract In this paper computation of the solution for the H∞ model reduction problem is addressed. Two LMI based computational schemes are developed. The computational schemes are based on a recent characterization of the solution for the optimal H∞ model reduction problem. Examples are given to illustrate the results.