Nonlinear Control Sy.. - Free

7.6. EXERCISES 199
(i) Is it locally input-to-state-stable?
(ii) Is it input-to-state-stable?
(7.9) Consider the following cascade connection of systems:
(i) Is it locally input-to-state-stable?
(ii) Is it input-to-state-stable?
Notes and References
-21 + 222 + 71,1
-22 + U2
-Z3 + 2221 - Z22 + 2122
The concept of input-to-state stability, as presented here, was introduced by Sontag [69].
Theorems 7.3 and 7.6 were taken from reference [73]. The literature on input-to-state
stability is now very extensive. See also References [70], [74], [71], and [72] for a thorough
introduction to the subject containing the fundamental results. See also chapter 10 of
Reference [37] for a good survey of results in this area. ISS pairs were introduced in
Reference [75]. Section 7.5 on cascade connection of ISS systems, as well as Theorems 7.7
and 7.8 are based on this reference.