Zero dynamics and funnel control of linear differential-algebraic systems
Please always quote using this URN:urn:nbn:de:0296-matheon-7297
- We study the class of linear differential-algebraic m-input m-output systems which have a transfer function with proper inverse. A sufficient condition for the transfer function to have proper inverse it that the system has 'strict and non-positive relative degree'. We present two main results: First, a so called 'zero dynamics form' is derived: this form is - within the class of system equivalence - a simple "almost normal" form of the DAE; it is a counterpart to the well-known Byrnes-Isidori form for ODE systems with strictly proper transfer function. The 'zero dynamics form' is exploited to characterize structural properties such as asymptotically stable zero dynamics, minimum phase, and high-gain stabilizability. The zero dynamics are characterized by (A,E,B)-invariant subspaces. Secondly, it is shown that the 'funnel controller' (that is a static nonlinear output error feedback) achieves, for all DAE systems with asymptotically stable zero dynamics and transfer function with proper inverse, tracking of a reference signal by the output signal within a pre-specified funnel. This funnel determines the transient behaviour.
Author: | Timo Reis, Thomas Berger, Achim Ilchmann |
---|---|
URN: | urn:nbn:de:0296-matheon-7297 |
Referee: | Fredi Tröltzsch |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2010/11/23 |
Release Date: | 2010/11/22 |
Tag: | |
Institute: | Technische Universität Berlin |
MSC-Classification: | 93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Bxx Controllability, observability, and system structure / 93B52 Feedback control |
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Dxx Stability / 93D15 Stabilization of systems by feedback | |
Preprint Number: | 746 |