System identification based on distribution theory and wavelet transform

Abstract

A review of system identification based on distribution theory is given. By the Schwartz kernel theorem, to every continuous linear system there corresponds a unique distribution, called kernel distribution. Formulae using wavelet transform to access time--frequency information of kernel distributions are deduced. A new wavelet-based system identification method for health monitoring systems is proposed as an application of a discretized formula using stationary wavelet transform.

Keywords:

• System identification
• Distribution
• Wavelet transform
• Stationary wavelet
• 2000 Mathematics Subject Classifications: Primary 42C40
• Secondary 93B30, 46F12, 65T60

Acknowledgement

This research was partially supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology, Grant-in-Aid for Scientific Research (C), 15540170 (2003--2004), and by the Japan Society for the Promotion of Science, Japan-U.S. Cooperative Science Program (2003--2004).

Notes

Email: [email protected]

This article is in memory of Professor Michihiro Nagase.

This article is in memory of Professor Michihiro Nagase.

Email: [email protected]

Additional information

Notes on contributors

Akira Morimoto ‡

Email: [email protected] This article is in memory of Professor Michihiro Nagase. Email: [email protected]