Compute quadratic H∞ performance of polytopic or parameter-dependent system
[perf,P] = quadperf(ps,g,options)
The RMS gain of the time-varying system
| (1) |
is the smallest γ > 0 such that
| (2) |
for all input u(t) with bounded energy. A sufficient condition for Equation 2 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 1 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).