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Robust Exponential Stability Analysis of Uncertain Discrete Time‐Varying Linear Systems
Author(s) -
Yao Yu,
Liu Kai,
Balakrishnan Venkataramanan,
She Wenxue,
Zhang Jianhong
Publication year - 2014
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 - 10.1002/asjc.803
Subject(s) - exponential function , mathematics , computation , exponential stability , mathematical optimization , convergence (economics) , stability (learning theory) , exponential growth , control theory (sociology) , rate of convergence , linear programming , convex optimization , linear system , regular polygon , computer science , algorithm , key (lock) , nonlinear system , artificial intelligence , mathematical analysis , physics , geometry , control (management) , computer security , quantum mechanics , machine learning , economics , economic growth
Abstract This paper studies the robust exponential stability of uncertain discrete linear time‐varying ( UDLTV ) systems. The key tool is the recently proposed generating functions. It can be found that a class of improved generating functions ( IGFS ) can fully characterize the robust exponential stability of UDLTV systems, and the maximum exponential decay rate of system trajectories can be computed by the radius of convergence of the IGFS . Moreover, the application of convex optimization technique and dynamic programming method provides an effective algorithm for the computation of the IGFS . Finally, the numerical example illustrates the efficacy and advantage of the proposed approach.