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decay

Quadratic decay rate of polytopic or affine P-systems

Syntax

[drate,P] = decay(ps,options)

Description

For affine parameter-dependent systems

$E (p) \dot{x} = A (p) x, p (t) = (p_{1} (t), \dots, p_{n} (t)),$

or polytopic systems

$E (t) \dot{x} = A (t) x, (A, E) \in Co {(A_{1}, E_{1}), \dots, (A_{n}, E_{n})},$

decay returns the quadratic decay rate drate, i.e., the smallest α ∊ R such that

A^TQE + EQA^T < αQ

holds for some Lyapunov matrix Q > 0 and all possible values of (A, E). Two control parameters can be reset via options(1) and options(2):

If options(1)=0 (default), decay runs in fast mode, using the least expensive sufficient conditions. Set options(1)=1 to use the least conservative conditions.
options(2) is a bound on the condition number of the Lyapunov matrix P. The default is 109.

See Also

pdlstab | psys | quadstab

Introduced before R2006a

Robust Control Toolbox Documentation

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