No abstract

An integral quadratic constraints (IQC) is introduced for stability analysis of linear systems with slowly varying parameters. The parameters are assumed to be bounded and with bounded derivatives. Other types of uncertainties can be included in the problem. The new criterion yields signi cantly less conservative bounds than previously proposed criteria.

Abstract-In order to meet the requirements for autonomous systems in real world applications, reliable path following controllers have to be designed to execute planned paths despite the existence of disturbances and model errors. In this paper we propose a Linear Quadratic controller for stabilizing a 2-trailer system with possible off-axle hitching around preplanned paths in backward motion. The controller design is based on a kinematic model of a general 2-trailer system including the possibility for off-axle hitching. Closed-loop stability is proved around a set of paths, typically chosen to represent the possible output from the path planner, using theory from linear differential inclusions. Using convex optimization tools a single quadratic Lyapunov function is computed for the entire set of paths.

The use of an over-parametrized state-space model for system identification has some clear advantages: A single model structure covers the entire class of multivariable systems up to a given order. The over-parametrization also leads to the possibility to choose a numerically stable parametrization. During the parametric optimization the gradient calculations constitute the main computational part of the algorithm. Consequently using more than the minimal number of parameters required slows down the algorithm. However, we show that for any chosen (over)-parametrization it is possible to reduce the gradient calculations to the minimal amount by constructing the parameter subspace which is orthonormal to the tangent space of the manifold representing equivalent models.

This paper presents an iterative t wo-step LMI method for improving the H 1 model error compared to Hankel norm reduction. The improvement of the Hankel norm reduced model is usually not signicant, typically a few percents only. For practical use the LMI reduction scheme is usually not worth-while, but it can be interresting from the theoretical and principal point of view.