Model reduction by moment matching for convergent Lur'e-type models

This paper proposes an approach to model order reduction of convergent Lur'e-type models, which consist of a linear time-invariant (LTI) block and a static nonlinear block that is placed in feedback with the LTI block. In the proposed approach, we match a finite number of moments of the LTI block and keep the static nonlinear block to approximate the moments of the Lur'e-type model. The benefits of this approach are that the Lur'e-type structure is preserved after reduction, that the reduction method has an interpretation in terms of the frequency response function of the LTI block and that global exponential stability properties of the full-order model are preserved. The effectiveness of the approach is illustrated in a numerical example

Optimal H∞ LMI-based model reduction by moment matching for linear time-invariant models

This paper proposes an approach to model order reduction of stable linear time-invariant (LTI) models. The proposed approach extends time-domain moment matching by the minimization of the H∞ norm of the error dynamics characterizing the difference between the full-order and reduced-order models given fixed interpolation points. The optimal H∞ moment matching problem is a constrained optimization problem with bilinear constraints. Introducing a novel numerical procedure, we minimize the approximation error, while respecting the constraints and, thereby, find a suboptimal H∞ reduced-order model. The effectiveness of the approach is illustrated in a numerical example

On global properties of passivity-based control of an inverted pendulum,”

SUMMARY The paper adresses the problem of stabilization of a speci"c target position of underactuated Lagrangian or Hamiltonian systems. We propose to solve the problem in two steps: "rst to stabilize a set with the target position being a limit point for all trajectories originating in this set and then to switch to a locally stabilizing controller. We illustrate this approach by the well-known example of inverted pendulum on a cart. Particularly, we design a controller which makes the upright position of the pendulum and zero displacement of the cart a limit point for almost all trajectories. We derive a family of static feedbacks such that any solution of the closed loop system except for those originating on some two-dimensional manifold approaches an arbitrarily small neighbourhood of the target position. The proposed technique is based on the passivity properties of the inverted pendulum. A possible extension to a more general class of underactuated mechanical systems is discussed