This directory contains some Matlab files that demonstrates algorithms
for LTV H-infty synthesis, as described in the report LiTH-ISY-R 3085,
2015-05-20.

This example is defined in plant0, which generates the LTV system at
different times:

>> [p, dim, gam] = plant0 (t);

p is the augmented system to be controlled, dim is the number of
controller inputs and outputs and gam is the H-infty gain, which can be
time varying.

We first generate the solutions to the Riccati DAEs in [0,15] seconds.
The FX solution is generated by a positive T (tend), while the FY
solution by a negative T.

>> [sol.t, sol.xi, sol.dxi] = hamint (@plant0, 15, 2*eye(4));
>> [sol.t, sol.yi, sol.dyi] = hamint (@plant0, -15);

Next, we need check the eigenvalues of X*Y:
>> ee = checkxy (sol.xi, sol.yi);
>> min (ee)

Here min(ee) should larger than 0, in this case 1.8061-06

If this does not hold, we need to adjust the plant (weighting functions),
P_0, P_T or gamma or combinations thereof.

We can now generate the LTV controler for an arbitraty instant in [0,15]
for instance at t = 1:

>> k = ltvsyn (@plant0, sol, 1)

Version 2015-09-02, Anders Helmersson, ISY, Linköpings universitet.