A Numerical Sufficiency Test for the Asymptotic Stability of Linear Time-Varying Systems

A numerical sufficiency test for the asymptotic stability of linear time-varying Hurwitz systems is proposed. The algorithmic procedure constructs a bounding tube in which the state is guaranteed to stay. The continuous-time system is evaluated at discrete time instants, for which successive quadratic Lyapunov functions are generated. The tube is constructed based on: (i) a conservative estimate of the state evolution, from a discrete time instant to the next, obtained from the corresponding Lyapunov function, and (ii) re-evaluation of the tube diameter at each discrete time instant to account for variations in the plant matrix. The numerical test is illustrated in simulation via both a stable and an unstable system.


Published in:
Automatica, 43, 4, 631-638
Year:
2007
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 Record created 2005-11-15, last modified 2018-01-27

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