Model reduction of LFT systems
- 9 December 2002
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 1233-1238 vol.2
- https://doi.org/10.1109/cdc.1991.261574
Abstract
The notion of balanced realizations and balanced truncation model reduction, including guaranteed error bounds, is extended to general Q-stable linear fractional transformations (LFTs). Since both multidimensional and uncertain systems are naturally represented using LFTs, this can be interpreted either as doing state order reduction for multidimensional systems or as uncertainty simplification in the case of uncertain systems. The role of Lyapunov equations in the 1D theory is replaced by linear matrix inequalities (LMIs). All proofs are given in detail as they are very short and greatly simplify even the standard 1D case.Keywords
This publication has 9 references indexed in Scilit:
- An improved error estimate for reduced-order models of discrete-time systemsIEEE Transactions on Automatic Control, 1990
- Quadratic stability with real and complex perturbationsIEEE Transactions on Automatic Control, 1990
- An algorithm for model reduction of 2-D discrete time systemsIEEE Transactions on Circuits and Systems, 1990
- The Lyapunov equation for n-dimensional discrete systemsIEEE Transactions on Circuits and Systems, 1988
- Stability and the matrix Lyapunov equation for discrete 2-dimensional systemsIEEE Transactions on Circuits and Systems, 1986
- Comments on "Stability for Two-Dimensional Systems via a Lyapunov ApproachIEEE Transactions on Circuits and Systems, 1985
- A transformation approach to stochastic model reductionIEEE Transactions on Automatic Control, 1984
- All optimal Hankel-norm approximations of linear multivariable systems and theirL,∞-error bounds†International Journal of Control, 1984
- Principal component analysis in linear systems: Controllability, observability, and model reductionIEEE Transactions on Automatic Control, 1981