๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Piecewise Riccati equations and the bounded real lemma

โœ Scribed by J. William Helton; Wei Zhan

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
149 KB
Volume
7
Category
Article
ISSN
1049-8923

No coin nor oath required. For personal study only.

โœฆ Synopsis

This article concerns peicewise linear systems and determining if they meet given H performance specifications. Such problems occur in control of linear systems with saturation nonlinearities. While one could imagine many mathematically natural piecewise linear systems we took care to extract one which does correspond to control of saturated plants. We think many such problems will fall into the category treated here. After a serious compromise (which makes our test for meeting specifications conservative), we arrive at a type of piecewise Riccati inequality. We show how these can be converted to matrix inequalities which are linear in the unknowns. Thus modern methods for optimizing such expressions can be used to obtain solutions.

๐Ÿ“œ SIMILAR VOLUMES

Stability and performance in the presenc
Stability and performance in the presence of magnitude bounded real uncertainty: Riccati equation based state space approaches
โœ Dragan Obradovic; Lena Valavani ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 353 KB

This paper is concerned with Riccati equation based analysis methods for determining stability and performance of perturbed feedback systems. The elements of the state-space representation of the systems are assumed to be linearly perturbed with real, magnitude bounded uncertaintites. Performance is

New solution bounds for the discrete alg
New solution bounds for the discrete algebraic matrix Riccati equation
โœ Chien-Hua Lee; Tsung-Lieh Hsien ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 96 KB ๐Ÿ‘ 2 views

New upper and lower matrix bounds and the corresponding eigenvalue bounds on the solution of the discrete algebraic Riccati equation are discussed in this paper. The present bounds are tighter than the majority of those found in the literature.

An explicit method for computing the pos
An explicit method for computing the positive real lemma matrices
โœ Nader Sadegh; John D. Finney; Bonnie S. Heck ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 189 KB

This paper presents an explicit non-iterative method for computing the positive real matrices and Youla's spectral factorization of a MIMO SPR system. All the computations are performed based on a minimal state space realization (A, B, C, D) with no restriction on D. The algorithm is tested on a sev