Title :
Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle and Popov theorems and their application to robust stability
Author :
Haddad, Wassim M. ; Bernstein, Dennis S.
Author_Institution :
Florida Inst. of Technol., Melbourne, FL, USA
Abstract :
Lyapunov function proofs of sufficient conditions for asymptotic stability are given for feedback interconnections of bounded real and positive real transfer functions. Two cases are considered: a proper bounded real (resp., positive real) transfer function with a bounded real (resp., positive real) time-varying memoryless nonlinearity; and two strictly proper bounded real (resp., positive real) transfer functions. A similar treatment is given for the circle and Popov theorems. Application of these results to robust stability with time-varying bounded real, positive real, and sector-bounded uncertainty is discussed
Keywords :
Lyapunov methods; stability criteria; transfer functions; Popov theorems; asymptotic stability; circle criterion; feedback interconnections; positive real transfer functions; positive real uncertainty; positively theorem; quadratic Lyapunov functions; robust stability; sector-bounded uncertainty; small gain theorem; strictly proper bounded real transfer functions; time-varying bounded real uncertainty; time-varying memoryless nonlinearity; Asymptotic stability; Electrostatic precipitators; Feedback; Linearity; Lyapunov method; Negative feedback; Robust stability; Stability analysis; Sufficient conditions; Transfer functions; Uncertainty;
Conference_Titel :
Decision and Control, 1991., Proceedings of the 30th IEEE Conference on
Conference_Location :
Brighton
Print_ISBN :
0-7803-0450-0
DOI :
10.1109/CDC.1991.261825
