Mid Semester Assignment on LMI of Lure’s problem
1. Based on Lyapunov stability condition, derive linear matrix inequalities’ (LMIs)
formulation from Lure’s problem depicted in the left hand-figure below in which (A,
B,C, D) is the state space model of the generalised plant, G(s).
2. Knowing the relation between saturation and deadzone, if the left hand-figure is
equivalent to the right hand-figure, what is the state space representation of Gp(s) in
terms of (A, B,C, D) matrices. Hint: the output of deadzone v is equal to the input of
saturation u substracted by the output of saturation uhat (see the figure below)
G p (s )
G (s )

u
u
 (.)
saturation
v
u
dz (.)
deadzone