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.

We analyze and design H-infinity controllers for general time-delay systems with time-delays in systems' state, inputs and outputs. We allow the designer to choose the order of the controller and to introduce constant time-delays in the controller. The closed-loop system of the plant and the controller is modeled by a system of delay differential algebraic equations (DDAEs). The advantage of the DDAE modeling framework is that any interconnection of systems and controllers prone to various types of delays can be dealt with in a systematic way, without using any elimination technique. We present a predictor-correct algorithm for the H-infinity norm computation of systems described by DDAEs. Instrumental to this we analyze the properties of the H-infinity norm. In particular, we illustrate that it may be sensitive with respect to arbitrarily small delay perturbations. Due to this sensitivity, we introduce the strong H-infinity norm which explicitly takes into account small delay perturbations, inevitable in any practical control application. We present a numerical algorithm to compute the strong H-infinity norm for DDAEs. Using this algorithm and the computation of the gradient of the strong H-infinity norm with respect to the controller parameters, we minimize the strong H-infinity norm of the closed-loop system based on non-smooth, non-convex optimization methods. By this approach, we tune the controller parameters and design H-infinity controllers with a prescribed order or structure.The time-delays τ i , i = 1, . . . , m are positive real numbers and the capital letters are real-valued matrices with appropriate dimensions. The input w and output z are disturbances and signals to be minimized to achieve design requirements and some of the system matrices include the controller parameters.

This paper considers black-and grey-box continuous-time transfer function estimation from frequency response measurements. The first contribution is a bilinear mapping of the original problem from the imaginary axis onto the unit disk. This improves the numerics of the underlying Sanathanan-Koerner iterations and the more recent instrumental-variable iterations. Orthonormal rational basis functions on the unit disk are utilized. Each iteration step necessitates a minimal state-space realization with these basis functions. One such derivation is the second contribution. System identification with these basis functions yield zero-pole-gain models. The third contribution is an efficient method to express transfer function coefficient constraints in terms of the orthonormal rational basis functions. This allows for estimating transfer function models with arbitrary relative degrees (including improper models), along with other fixed and bounded parameter values. The algorithm is implemented in the tfest function in System Identification Toolbox (Release 2016b, for use with MATLAB) for frequency domain data. Two examples are presented to demonstrate the algorithm performance.

We report on our experience with fixed-order H ∞ controller design using the HIFOO toolbox. We applied HIFOO to various benchmark fixed (or reduced) order H ∞ 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 H ∞ controller design.

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