Premium
STABILITY ANALYSIS OF UNCERTAIN DISCRETE‐TIME SYSTEMS WITH TIME‐VARYING STATE DELAY: A PARAMETER‐DEPENDENT LYAPUNOV FUNCTION APPROACH
Author(s) -
Gao Huijun,
Lam James,
Chen Tongwen,
Wang Changhong
Publication year - 2006
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1111/j.1934-6093.2006.tb00296.x
Subject(s) - control theory (sociology) , lyapunov function , stability (learning theory) , discrete time and continuous time , mathematics , constant (computer programming) , function (biology) , state (computer science) , time domain , computer science , nonlinear system , control (management) , algorithm , statistics , physics , quantum mechanics , artificial intelligence , machine learning , evolutionary biology , biology , programming language , computer vision
This paper presents several new robust stability conditions for linear discrete‐time systems with polytopic parameter uncertainties and time‐varying delay in the state. These stability criteria, derived by defining parameter‐dependent Lyapunov functions, are not only dependent on the maximum and minimum delay bounds, but also dependent on uncertain parameters in the sense that different Lyapunov functions are used for the entire uncertainty domain. It is established, theoretically, that these robust stability criteria for the nominal and constant‐delay case encompass some existing result as their special case. The delay‐dependent and parameter‐dependent nature of these results guarantees the proposed robust stability criteria to be potentially less conservative.