Nonlinear Stochastic Control and Filtering with Engineering-Oriented Complexities by Guoliang Wei & Zidong Wang & Wei Qian

Author:Guoliang Wei & Zidong Wang & Wei Qian
Language: eng
Format: epub
Publisher: CRC Press

From (7.3)–(7.5) and (7.14), it can be seen that

where (k) = [xT(k) xT(k−d) and

with

In the following, we are going to show that Ω < 0 can be concluded from (7.10). To do this, we Premultiply and postmultiply the LMIs in (7.10) by diag{S−T, S−T, I, S−T, σ−2S−T, and its transpose, and we can obtain

with −Q(p(k+1))+S−1+S−T.

Let us now show that, if (7.18) holds, then the LMIs

where and Πk+1 =Q−1(p(k+1)), are true.

If (7.18) holds, we can know from −Q(p(k +1)) +S−1 +S−T > 0 that S−1 is a nonsingular matrix. By performing the congruence transformation diag{I, I, I, S, S, S} to (7.18), we can have

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.