Robust Control Toolbox™

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

(5-22)

is the smallest > 0 such that

(5-23)

for all input u(t) with bounded energy. A sufficient condition for (9-23) is the existence of a quadratic Lyapunov function

V(x) = x^TPx, P > 0

such that

Minimizing 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 (9-22) 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).

See Also
quadstab    Quadratic stability of polytopic or affine parameter-dependent systems

psys        Specification of uncertain state-space models

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