GRADIENT ALGORITHMS for COMMON LYAPUNOV FUNCTIONS

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GRADIENT ALGORITHMS for COMMON LYAPUNOV
FUNCTIONS
Daniel Liberzon Univ. of Illinois at
Urbana-Champaign, U.S.A.
Roberto Tempo IEIIT-CNR, Politecnico di Torino,
Italy
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PROBLEM
Motivation stability of uncertain and switched
systems
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MOTIVATING EXAMPLE
Nonlinear extensions Shim et al. (1998), Vu L
(2003)
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ITERATIVE ALGORITHMS PRIOR WORK
Algebraic inequalities
Agmon, Motzkin, Schoenberg (1954) Polyak
(1964) Yakubovich (1966)
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GRADIENT ALGORITHMS PRELIMINARIES
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GRADIENT ALGORITHMS PRELIMINARIES
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GRADIENT ALGORITHMS DETERMINISTIC CASE
visits each index times
Gradient iteration
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GRADIENT ALGORITHMS PROBABILISTIC CASE
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SIMULATION EXAMPLE
Interval family of triangular Hurwitz matrices
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CONCLUSIONS
Contribution

• Gradient iteration algorithms for solving
• simultaneous Lyapunov matrix inequalities
• Deterministic convergence for finite families,
• probabilistic convergence for infinite families