# Documentation

Compute quadratic H performance of polytopic or parameter-dependent system

## Syntax

```[perf,P] = quadperf(ps,g,options)
```

## Description

The RMS gain of the time-varying system

 (2-20)

is the smallest γ > 0 such that

 ${‖y‖}_{{L}_{2}}\le \gamma {‖u‖}_{{L}_{2}}$ (2-21)

for all input u(t) with bounded energy. A sufficient condition for Equation 2-21 is the existence of a quadratic Lyapunov function

V(x) = xTPx, P > 0

such that

Minimizing γ over such quadratic Lyapunov functions yields the quadratic H performance, an upper bound on the true RMS gain.

The command

```[perf,P] = quadperf(ps) ```

computes the quadratic H performance `perf` when Equation 2-20 is a polytopic or affine parameter-dependent system `ps` (see `psys`). The Lyapunov matrix P yielding the performance `perf` is returned in `P`.

The optional input `options` gives access to the following task and control parameters:

• If `options(1)=1`, `perf` is the largest portion of the parameter box where the quadratic RMS gain remains smaller than the positive value `g` (for affine parameter-dependent systems only). The default value is 0.

• If `options(2)=1`, `quadperf` uses the least conservative quadratic performance test. The default is `options(2)=0` (fast mode)

• `options(3)` is a user-specified upper bound on the condition number of P (the default is 109).