We propose a method for model reduction on a given frequency range, without the use of input and output filter weights. The method uses a nonlinear optimization approach to minimize a frequency limited H 2 like cost function. An important contribution of the paper is the derivation of the gradient of the proposed cost function. The fact that we have a closed form expression for the gradient and that considerations have been taken to make the gradient computationally efficient to compute enables us to efficiently use off-the-shelf optimization software to solve the optimization problem.

In this paper we have formulated the problem of finding an LPV-approximation to a system as an optimization problem. For this optimization problem we have presented two possible ways to solve this. The problem is posed as a model reduction problem and formulated such that it should try to preserve the input-output behavior of the system. In the two examples in the paper the potential of the new methods are shown. We have also shown the benefits of using model reduction techniques to capture the input-output behavior to obtain accurate low order LPV-approximations. One method uses SDP-optimization to solve the problem. SDP-optimization has been a hot topic during the last years, but the problem with the SDP method is that it scales badly with the dimension of the problem. Also here it has bilinear constraints which makes the problem really difficult. With the other method we try to use a more general nonlinear approach which seem to be more suitable for this problem. For this method we have also calculated a gradient that can be used to apply a descent or Newton-like method to solve the problem.

Controller synthesis for linear parameter varying (lpv) systems has received a lot of attention from the control community. This is mainly motivated by the wide range of non-linear dynamical systems that can be approximated by lpv-systems. In this paper a novel method is presented that, by only using local state space models as data, tries to solve the problem of finding a linear parameter varying output-feedback controller. The method uses non-linear programming and a quasi-Newton framework to solve the problem. The great advantages with the proposed method is that it is possible to impose structure in the controller and that you do not need an lpv-model, only state space models for different values of the scheduling parameters. Finally an example is presented to show the potential of the method.

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A method to identify LPV-models through minimization of an H 2 -norm objective is presented. The method uses a direct nonlinear programming approach to a non-convex problem. The reason to use H 2 -norm is twofold. To begin with, it is a well known and widely used system norm and secondly, the cost functions described in this paper becomes differentiable when using the H 2 -norm. This enables us to have a measure of first order optimality and to use standard quasi-Newton solvers to solve the problem. The specific structure of the problem is utilized in great detail to compute cost functions and gradients efficiently. Additionally, a regularized version of the method, which also has a nice computational structure, is presented. The regularized version is shown to have an interesting interpretation with connections to worst-case approaches.