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STABILITY OF LINEAR TIME‐INVARIANT OPEN‐LOOP UNSTABLE SYSTEMS WITH INPUT SATURATION
Author(s) -
Wang WenLiang A.,
Mukai Hiro
Publication year - 2004
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.1934-6093.2004.tb00370.x
Subject(s) - stability theory , mathematics , control theory (sociology) , lti system theory , saturation (graph theory) , invariant (physics) , lyapunov function , linear system , exponential stability , lyapunov stability , mathematical analysis , nonlinear system , control (management) , computer science , physics , combinatorics , mathematical physics , quantum mechanics , artificial intelligence
This paper analyzes the stability of a linear time‐invariant open‐loop unstable system subject to input saturation. First, we extend the idea of approximating the locally asymptotically stable region (controllable set) of the system for the case where the control is small enough to be unsaturated (inside the linear region), to the case when the control is allowed to saturate. It is shown that, when the Lyapunov descent criterion and the Kuhn‐Tucker Theorem is applied, a superior locally asymptotically stable region is found. A technique for approximating the locally asymptotically stable region is presented.