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On the existence of common quadratic Lyapunov functions for second‐order linear time‐invariant discrete‐time systems
Author(s) -
Akar Mehmet,
Narendra Kumpati S.
Publication year - 2002
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.720
Subject(s) - lyapunov function , mathematics , constructive , discrete time and continuous time , quadratic equation , lti system theory , lyapunov equation , invariant (physics) , verifiable secret sharing , linear system , order (exchange) , control theory (sociology) , mathematical analysis , nonlinear system , computer science , control (management) , process (computing) , artificial intelligence , mathematical physics , operating system , geometry , quantum mechanics , statistics , physics , programming language , set (abstract data type) , finance , economics
Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function (CQLF) are given for two second‐order linear time‐invariant discrete‐time systems. These conditions are later extended to an arbitrary number of systems. The conditions are readily verifiable both analytically and graphically. The paper also provides a constructive procedure for computing a CQLF when it exists. Copyright © 2002 John Wiley & Sons, Ltd.