Premium
Robust stability of large‐scale systems which contain time‐invariant lur'e‐type uncertainties in subsystems and norm‐bounded uncertainties in interconnections
Author(s) -
Saeki Masami,
Araki Mituhiko
Publication year - 1994
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4590040606
Subject(s) - lyapunov function , mathematics , bounded function , nonlinear system , control theory (sociology) , norm (philosophy) , scalar (mathematics) , lyapunov exponent , invariant (physics) , mathematical analysis , computer science , control (management) , physics , geometry , quantum mechanics , artificial intelligence , political science , law , mathematical physics
In this paper a new frequency‐domain condition for the robust stability of a class of large‐scale systems is derived. It is assumed that each subsystem contains one time‐invariant nonlinearity satisfying a sector condition, and that the interconnecting functions are linearly bounded by the norms of the scalar outputs of subsystems. In deriving the above such Lur'e‐type Lyapunov functions of subsystems are constructed so that their weighted sum is a Lyapunov function of the overall system. This condition is potential to give a sharper result than the circle‐condition‐type result which was obtained previously. Furthermore, a method to estimate the domain of attraction using the above Lyapunov function is also given when the sector condition is satisfied only locally.