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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)$\stackrel{˙}{x}$ = A(p)x, p(t) = (p1(t), . . . , pn(t))

or polytopic systems

E(t)$\stackrel{˙}{x}$ = A(t)x, (A, E) ∊ Co{(A1, E1), . . ., (An, En)}, t)$\stackrel{˙}{x}$ = A(t)x, (A, E) ∊ Co{(A1, E1), . . ., (An, En)},

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

ATQE + EQAT < 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.