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Input to state stabilizability for parametrized families of systems
Author(s) -
Lin Yuandan,
Sontag Eduardo D.,
Wang Yuan
Publication year - 1995
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.4590050304
Subject(s) - bounded function , cascade , stability (learning theory) , state (computer science) , state space , control theory (sociology) , mathematics , lyapunov function , characterization (materials science) , set (abstract data type) , lyapunov stability , computer science , control (management) , algorithm , nonlinear system , artificial intelligence , engineering , mathematical analysis , statistics , physics , materials science , quantum mechanics , machine learning , chemical engineering , programming language , nanotechnology
This paper studies various stability issues for parametrized families of systems, including problems of stabilization with respect to sets. The study of such families is motivated by robust control applications. A Lyapunov‐theoretic necessary and sufficient characterization is obtained for a natural notion of robust uniform set stability; this characterization allows replacing ad hoc conditions found in the literature by more conceptual stability notions. We then use these techniques to establish a result linking state‐space stability to ‘input to state’ (bounded‐input bounded‐state) stability. In addition, the preservation of stabilizability under certain types of cascade interconnections is analysed.