1. FEEDBACK SYSTEMS: ABSOLUTE STABILITY
controllable
Circle criterion: quadratic common Lyapunov function
is strictly positive real (SPR):
Common way in which a switched system arises
Switched system is GUES
Discuss passivity a little more, mention KYP (see notes)
More on Popov later
For this reduces to SPR (passivity)
Popov criterion not suitable: depends on

2. FEEDBACK SYSTEMS: SMALL-GAIN THEOREM
controllable
Small-gain theorem:
quadratic common Lyapunov function
Again, switched system is GUES
Can handle norms other than 1 (clear)

3. TWO-DIMENSIONAL SYSTEMS
Necessary and sufficient conditions for GUES
known since 1970s
worst-case
switching
Planar geometry: explain briefly worst-case switching – already mentioned earlier
quadratic common Lyap fcn <=>
convex combinations of Hurwitz