## H-inf. loop shaping design procedure routines in SLICOT

### Da-Wei Gu, Petko Hr. Petkov and Mihail Konstantinov

NICONET Report 1999-15: November 1999.

This report briefly introduces the H-inf. loop shaping design procedure (LSDP) and its implementation in the software package SLICOT. The developed routines are tested in a design example and are included as appendices.

## Numerical problems in robust and H-inf optimal control

### Anton A. Stoorvogel

NICONET Report 1999-13: September 1999.

After formulating the H_inf control problem for linear, time-invariant and finite-dimensional systems, the difficulties in the computation of the optimal performance are discussed, as well as the problems encountered in computing controllers.

## H-inf and H2 optimization toolbox in SLICOT

### Da-Wei Gu, Petko Hr. Petkov and Mihail Konstantinov

SLICOT Working Note 1999-12: September 1999.

This report summarizes the progress made in the sub-task IV.A of the NICONET project. Selected routines to implement H_inf and H_2 (sub) optimization syntheses are listed, which have all been standardized and included in the SLICOT package. The integration of those routines in MATLAB has also been completed; the MEX-files are attached in the appendices. This report discusses the selection and testing of benchmark problems with regard to the developed routines, and the comparisons made between these routines and others available in MATLAB. In particular, two industrial benchmark case studies, namely the controller design of a Bell 205 helicopter and a distillation column design, are introduced and the design results, obtained using the developed routines, are analysed.

## A MATLAB MEX-file environment of SLICOT

### Volker Mehrmann, Vasile Sima, Andras Varga and Hongguo Xu

SLICOT Working Note 1999-11: August 1999.

Several MEX-files are developed based on SLICOT Fortran subroutines. The MEX-files provide new tools for the numerical solution of some classical control problems such as the solution of linear or Riccati matrix equations computations in the MATLAB environment. Numerical tests show that the resulting MEX-files are equally accurate and much more efficient than the corresponding MATLAB functions in the control system toolbox and the robust control toolbox. In order to increase user-friendlyness the related m-files are also developed so that the MEX-file interface to the corresponding SLICOT routines can be implemented directly and easily.

## Numerical solution of matrix Riccati equations: a comparison of six solvers

### Petko Petkov, Mihail Konstantinov, Da-Wei Gu, Volker Mehrmann

NICONET Report 1999-10: August 1999.

We present results from the evaluation of six solvers intended for the numerical solution of continuous-time matrix algebraic Riccati equations. The solvers include the MATLAB functions from different toolboxes and two Fortran 77 solvers developed by the authors. The comparison implements two benchmark problems each comprising 1600 6-th order Riccati equations with known solutions. For each solver and each equation we compute the relative forward and backward errors and for two of the solvers we investigate the accuracy of condition and error estimates. Some conclusions concerning the numerical behaviour of the solvers are given.