Concepts of Strict Positive Realness and the Absolute Stability Problem of Continuous-Time Systems

Automatica ◽  
1998 ◽  
Vol 34 (9) ◽  
pp. 1071-1082 ◽  
Author(s):  
CHENGSHAN XIAO ◽  
DAVID J. HILL
Keyword(s):  
Continuous Time ◽  
Stability Problem ◽  
Absolute Stability ◽  
Continuous Time Systems ◽  
Positive Realness ◽  
The Absolute ◽  
Time Systems ◽  
Absolute Stability Problem

scholarly journals Absolute stability of a class of fractional positive nonlinear systems

2019 ◽  
Vol 29 (1) ◽  
pp. 93-98 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Absolute Stability ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Discrete Time Systems ◽  
The Absolute ◽  
Necessary And Sufficient ◽  
Time Systems

Abstract The positivity and absolute stability of a class of fractional nonlinear continuous-time and discrete-time systems are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of fractional positive nonlinear systems are also given.

Regions of exponential stability for the problem of Lur’e / Bereiche der exponentiellen Stabilität beim Problem von Lurje

1969 ◽  
Vol 17 (1) ◽  
Author(s):  
D. Siljak ◽  
S. Weissenberger
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Stability Problem ◽  
Absolute Stability ◽  
Nonlinear Characteristics ◽  
Forcing Function ◽  
Nonautonomous Differential Equations ◽  
The Absolute ◽  
Absolute Stability Problem

This paper proposes a method for computing finite regions of exponential stability from solutions of the absolute stability problem. A best quadratic estimate of the regions is found for a class of nonlinear characteristics which belong to a modified Lur’e sector. For a class of nonautonomous differential equations, a bound on the forcing function is found which guarantees that all the corresponding solutions remain inside the computed region.

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