QuadraticOutputStateSpace{T}

An object representing a quadratic output state space system.

dx(t)/dt = Ax(t) + Bu(t)
y(t)     = Cx(t) + M(x(t)⊗x(t))

See the function qoss for a user facing constructor.

Fields:

• A::Matrix{T}
• B::Matrix{T}
• C::Matrix{T}
• M::Matrix{T}

X = gram(Σqo::QuadraticOutputStateSpace, opt::Symbol; kwargs...)

Returns the Gramian of system Σqo. If opt is :c the controllability Gramian is computed. If opt is :o the observability Gramian is computed.

L = grampd(Σqo::QuadraticOutputStateSpace, opt::Symbol; kwargs...)

Returns a Cholesky factor L of the Gramian of system Σqo. If opt is :c, the controllability Gramian P=L'*L is computed. If opt is :o the observability Gramian Q=L*L' is computed.

result = lsim(Σqo, u, t; kwargs...)

Calculate the time response of the quadratic output state-space model Σqo::QuadraticOutputStateSpace{T} by first treating it as standard state-space model and calling ControlSystems.lsim on it, and then calculating the quadratic part of the output and add it to the linear par.

norm(Σqo, p=2; kwargs...)
h2norm(Σqo; kwargs...)

Computes the H2 norm of the quadratic output state-space model Σqo::QuadraticOutputStateSpace.

h2inner(Σ1, Σ2)

Computes the H2 inner product of the quadratic output state-space models Σ1::QuadraticOutputStateSpace and Σ2::QuadraticOutputStateSpace.

Σqo = qoss(A, B, C, M)
Σqo = qoss(A, B, M)

Creates a quadratic output state-space model Σqo::QuadraticOutputStateSpace{T} with matrix element type T.