On the positivity and stability of non-stationary systems

✍ Scribed by M.K. Sundareshan; M.A.L. Thathachar

• Publisher: Elsevier Science
• Year: 1976
• Tongue: English
• Weight: 706 KB
• Volume: 302
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(76)90043-0

✦ Synopsis

The positivity of operators in Hilbert spaces is an important concept finding wide application in various branches of Mathematical System Theory. A frequencydomain condition that ensures the positivity of time-varying operators in L2 with a state-space description, is derived in this paper by using certain newly developed inequalities concerning the input-state relation of such operators. As an interesting application

of these results, an L2 stability criterion for time-varying feedback systems consisting of a finite-sector non-linearity is also developed.