outputJacobian

Method of mss.

Compute the Jacobian of the output equations at an operating point.

Source: src/model/@mss/outputJacobian.m

Syntax

J = outputJacobian(sys, stateVector, inputVector)
J = sys.outputJacobian(x, u)

Description

outputJacobian is the output-equation counterpart of stateJacobian. It returns the first-order derivatives of

$$y = g(x,u)$$

with respect to the states and the inputs, evaluated at $(x,u)$:

$$J = \left[\ \frac{\partial g}{\partial x}\ \ \frac{\partial g}{\partial u}\ \right] \in \mathbb{R}^{\,n_\text{output}\times(n_\text{state}+n_\text{input})}.$$

The two blocks are the $C$ and $D$ matrices of a local linearization; linearize obtains them by splitting J at column nState.

As in stateJacobian, the signal vector is assembled by scattering $x$ and $u$ through stateIndex and inputIndex, and the resulting columns are reordered into the same signal order — column $k$ is the derivative with respect to state $k$, followed by the inputs — so any structure-matrix row layout works and J can be split at column nState. The tensor decides the evaluation path:

• CPNTensor — the consolidated jacobian entry point with equationIndex = outputEquationIndex and columnIndex = columnIndexOutputEq.
• Any other mtiTensor, e.g. TTTensor — the tensor’s own computeOutputJacobianMatrixMss.

Input arguments

Output arguments

Example

sys = rmss(3,1,1,4);
J = sys.outputJacobian([1; 0; -1], 0.5);

C = J(:, 1:sys.nState);        % output matrix
D = J(:, sys.nState+1:end);    % feedthrough matrix

See also

stateJacobian · linearize · outputValue · jacobian · mss

MyToolbox Documentation | Generated automatically by CI/CD pipeline