Robust Performance Bounds based on Lyapunov Functions for Uncertain Systems
Robust Performance Bounds based on Lyapunov Functions for Uncertain Systems
V. Balakrishnan
Proc. Annual Allerton Conf. on Communication, Control and Computing
pages 142-151, Allerton House, Monticello, Illinois, October 1996
Abstract:
The robust stability analysis of uncertain
systems, with various assumptions on the nature of the
uncertainties (sector-bounded nonlinear, linear
time-invariant, parametric, etc.), as well as their
structure (diagonal, block-diagonal, etc.), can be
performed in a unified manner using multiplier theory and
LMI-based convex optimization. The multipliers used in the
stability analysis can be shown to yield a convex
parametrization of a subset of Lyapunov functions that
provide a certificate of robust stability. We show how
these Lyapunov functions can in turn be used to derive bounds
on various robust performance measures of the system. We
illustrate our approach with three specific robust
performance analysis problems.
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