stateJacobian

Method of mss.

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

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

Syntax

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

Description

stateJacobian returns the first-order derivatives of the state equation

$$\dot x = f(x,u) \qquad\text{(or } x_{k+1} = f(x_k,u_k) \text{ for a discrete model)}$$

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

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

The two blocks are the $A$ and $B$ matrices of a local linearization; splitting J at column nState is exactly what linearize does. The operating point need not be an equilibrium.

The method assembles the full signal vector by scattering $x$ and $u$ through stateIndex and inputIndex, and reorders the resulting columns into the same signal order — column $k$ is the derivative with respect to state $k$, followed by the inputs. Both are needed for a model whose structure-matrix rows are not in the natural [x; u] order: the tensor returns one column per structure-matrix row, in row order, so without the reorder splitting J at column nState (which linearize does) would mix states and inputs. For a natural layout both steps are the identity.

The evaluation then dispatches on the tensor:

• CPNTensor — the consolidated jacobian entry point with equationIndex = stateEquationIndex and columnIndex = columnIndexStateEq, so only the state block’s rows and monomial columns are differentiated.
• Any other mtiTensor, e.g. TTTensor — the tensor’s own computeStateJacobianMatrixMss.

Input arguments

Output arguments

Example

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

A = J(:, 1:sys.nState);        % state matrix
B = J(:, sys.nState+1:end);    % input matrix

See also

outputJacobian · linearize · functionValue · jacobian · mss

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