LPVNORM - Compute bound on norm for pss systems.
Contents
Syntax
[Gamma,X] = lpvnorm(P) [Gamma,X] = lpvnorm(P,'L2') [Gamma,X] = lpvnorm(P,'LQG') [Gamma,X] = lpvnorm(P,Xb) [Gamma,X] = lpvnorm(P,Xb,'L2') [Gamma,X] = lpvnorm(P,Xb,'LQG')
Description
lpvnorm computes a bound on the norm of a pss system over the set of all permissible trajectories of the independend variables which the pss depends on.
[Gamma,X] = lpvnorm(P,'L2') computes an upper bound Gamma on the induced norm of the pss P. The upper bound Gamma and a constant (parameter independent) matrix X are computed to satisfy the induced norm linear matrix inequality (LMI) condition. X is returned as a pmat. The
norm bound is valid for arbitrarily fast variations of the system parameters.
[Gamma,X] = lpvnorm(P,'LQG') computes an upper bound Gamma on the stochastic LPV bound. The stochastic LPV bound is defined as the expected value of the average instantaneous power of the output of P, assuming its inputs are zero mean, white-noise processes with unit intensity.
[Gamma,X] = lpvnorm(P,Xb,ALG) computes a tighter (less conservative) bound on the norm by using a parameter dependent matrix X = and bounds on the parameter rates of variation. The basis functions used to construct
are specified with the basis object Xb. ALG can be either 'L2' or 'LQG'. A call without the ALG argument is equivalent to [Gamma,X] = lpvnorm(P,Xb,'L2').