— Function File: [g, gmin, gmax] = hinfnorm (sys, tol, gmin, gmax, ptol)

Computes the H-infinity norm of a system data structure.

Inputs

sys

system data structure

tol

H-infinity norm search tolerance (default: 0.001)

gmin

minimum value for norm search (default: 1e-9)

gmax

maximum value for norm search (default: 1e+9)

ptol

pole tolerance:

• if sys is continuous, poles with |real(pole))| < ptol*||H|| (H is appropriate Hamiltonian) are considered to be on the imaginary axis.
• if sys is discrete, poles with |abs(pole)-1| < ptol*||[s1,s2]|| (appropriate symplectic pencil) are considered to be on the unit circle.
• Default value: 1e-9

Outputs

g

Computed gain, within tol of actual gain. g is returned as Inf if the system is unstable.

gmin

gmax

Actual system gain lies in the interval [gmin, gmax].

References: Doyle, Glover, Khargonekar, Francis, State-space solutions to standard H-2 and H-infinity control problems, IEEE TAC August 1989; Iglesias and Glover, State-Space approach to discrete-time H-infinity control, Int. J. Control, vol 54, no. 5, 1991; Zhou, Doyle, Glover, Robust and Optimal Control, Prentice-Hall, 1996.