Compute quadratic H performance of polytopic or parameter-dependent system


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


The RMS gain of the time-varying system

E(t)x˙=A(t)x+B(t)u,   y=C(t)X+D(t)u(1-20)

is the smallest γ > 0 such that


for all input u(t) with bounded energy. A sufficient condition for Equation 1-21 is the existence of a quadratic Lyapunov function

V(x) = xTPx, P > 0

such that

uL2, dVdt+yTyγ2uTu<0

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 1-20 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).

See Also


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