ObservabilityGramian

ObservabilityGramian[ssm]
gives the observability Gramian of the state-space model ssm.

Details and OptionsDetails and Options

  • The state-space model ssm can be given as StateSpaceModel[{a,b,c,d}], where a, b, c, and d represent the state, input, output, and transmission matrices in either a continuous-time or a discrete-time system:
  • continuous-time system
    discrete-time system
  • The observability Gramian:
  • continuous-time system
    discrete-time system
  • For asymptotically stable systems, the Gramian can be computed as the solution of a Lyapunov equation:
  • continuous-time system
    discrete-time system
  • For a StateSpaceModel with a descriptor matrix, ObservabilityGramian returns a pair of matrices , where is associated with the slow subsystem, and is associated with the fast subsystem.
  • The observability Gramians only exist for descriptor systems in which Det[λ e-a]0 for some λ.
Introduced in 2010
(8.0)
| Updated in 2012
(9.0)