New Perspectives and Applications of Modern Control Theory by Julio B. Clempner & Wen Yu

Author:Julio B. Clempner & Wen Yu
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(10.79)

where

(10.80)

(10.81)

(10.82)

(10.83)

Proof

By Schur complement lemma, we get that (10.79) is equivalent to

(10.84)

It leads to

(10.85)

Let . Pre- and post multiplied by M(j), it gives

(10.86)

The Lyapunov function candidate is given as

(10.87)

The weak infinitesimal operator of the process at the point is given by

(10.88)

By (10.86), we get , if . Referring (10.70), it can be drawn that the system state is stochastically asymptotically stable. This completes the proof.

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