Suat Gumussoy

Multiobjective robust control with HIFOO 2.0

Abstract Multiobjective control design is known to be a difficult problem both in theory and practice. Our approach is to search for locally optimal solutions of a nonsmooth optimization problem that is built to incorporate minimization objectives and constraints for multiple plants. We report on the success of this approach using our public-domain matlab toolbox hifoo 2.0, comparing our results with benchmarks in the literature.

Combining Convex–Concave Decompositions and Linearization Approaches for Solving BMIs, With Application to Static Output Feedback

A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is linearized, leading to a convex subproblem. Applications to various output feedback controller synthesis problems are presented. In these applications, the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality (LMI) constraints. The performance of the algorithm has been benchmarked on the data from the COMPleib library.

Remarks on strong stabilization and stable H∞ controller design

A state space based design method is given to find strongly stabilizing controllers for multi-input-multi-output plants (MIMO). A sufficient condition is derived for the existence of suboptimal stable H/sup /spl infin// controller in terms of linear matrix inequalities (LMI) and the controller order is twice that of the plant. A new parameterization of strongly stabilizing controllers is determined using linear fractional transformations (LFT).

Fixed-order H ∞ controller design via HIFOO, a specialized nonsmooth optimization package

We report on our experience with fixed-order Hfrinfin controller design using the HIFOO toolbox. We applied HIFOO to various benchmark fixed (or reduced) order Hfrinfin controller design problems in the literature, comparing the results with those published for other methods. The results show that HIFOO can be used as an effective alternative to existing methods for fixed-order Hfrinfin controller design.

H ∞ strong stabilization via HIFOO, a package for fixed-order controller design

We report on our experience with strong stabilization using HIFOO, a toolbox for H^∞ fixed-order controller design. We applied HIFOO to 21 fixed-order stable H^∞ controller design problems in the literature, comparing the results with those published for other methods. The results show that HIFOO often achieves good H^∞ performance with low-order stable controllers, unlike other methods in the literature.

Coprime inner/outer factorization of SISO time-delay systems and FIR structure of their optimal H-infinity controllers

SUMMARY The approach in Foias et al. (Robust control of Infinite Dimensional: Frequency Domain Methods. Springer: Berlin, 1996) is one of the well-developed methods to design H-infinity controllers for general infinite dimensional systems. This approach is applicable if the plant admits a special coprime-inner/outer factorization. We give the largest class of single-input–single-output (SISO) time-delay systems for which this factorization is possible and factorize the admissible plants. Based on this factorization, we compute the optimal H-infinity performance and eliminate unstable pole-zero cancellations in the optimal H-infinity controller. We extend the results on the finite impulse response structure of optimal H-infinity controllers by showing that this structure appears not only for plants with input/output delays, but also for general SISO time-delay plants. Copyright

A predictor-corrector type algorithm for the pseudospectral abscissa computation of time-delay systems

The pseudospectrum of a linear time-invariant system is the set in the complex plane consisting of all the roots of the characteristic equation when the system matrices are subjected to all possible perturbations with a given upper bound. The pseudospectral abscissa is defined as the maximum real part of the characteristic roots in the pseudospectrum and, therefore, it is for instance important from a robust stability point of view. In this paper we present an accurate method for the computation of the pseudospectral abscissa of retarded delay differential equations with discrete pointwise delays. Our approach is based on the connections between the pseudospectrum and the level sets of an appropriately defined complex function. The computation is done in two steps. In the prediction step, an approximation of the pseudospectral is obtained based on a rational approximation of the characteristic matrix and the application of a bisection algorithm. Each step in this bisection algorithm relies on checking the presence of the imaginary axis eigenvalues of a complex matrix, similar to the delay free case. In the corrector step, the approximate pseudospectral abscissa is corrected to any given accuracy, by solving a set of nonlinear equations that characterizes the extreme points in the pseudospectrum contours.

Characterization and Computation of

We consider the characterization and computation of

\mathcal{H}_{\infty}

\mathcal{H}_{\infty}

Norms for Time-Delay Systems

norms for a class of time-delay systems. It is well known that in the finite-dimensional case the