New Schemes for Positive Real Truncation

• Main Authors: Kari Unneland, Paul Van Dooren, Olav Egeland
• Format: Article
• Language: English
• Published: Norwegian Society of Automatic Control 2007-07-01
• Series: Modeling, Identification and Control
• Subjects: Model Reduction; Balanced Truncation; Positive Realness
• Online Access: http://www.mic-journal.no/PDF/2007/MIC-2007-3-1.pdf
• ISSN: 0332-7353; 1890-1328

Model reduction, based on balanced truncation, of stable and of positive real systems are considered. An overview over some of the already existing techniques are given: Lyapunov balancing and stochastic balancing, which includes Riccati balancing. A novel scheme for positive real balanced truncation is then proposed, which is a combination of the already existing Lyapunov balancing and Riccati balancing. Using Riccati balancing, the solution of two Riccati equations are needed to obtain positive real reduced order systems. For the suggested method, only one Lyapunov equation and one Riccati equation are solved in order to obtain positive real reduced order systems, which is less computationally demanding. Further it is shown, that in order to get positive real reduced order systems, only one Riccati equation needs to be solved. Finally, this is used to obtain positive real frequency weighted balanced truncation.