linmod

📝Syntax

[A, B, C, D] = linmod(model)
[A, B, C, D] = linmod(model, x0, u0)
A = linmod(model)

📥Input Arguments

Parameter	Description
model	a loaded system (name or handle) or the path to a .nflow file.
x0	optional operating-point state (length nx). Absent: the post-INIT state.
u0	optional operating-point inputs (length nu). Absent: zero.

📤Output Arguments

Parameter	Description
A	the nx-by-nx state Jacobian d(xdot)/dx about the operating point.
B	the nx-by-nu input Jacobian d(xdot)/du about the operating point.
C	the ny-by-nx output Jacobian dy/dx about the operating point.
D	the ny-by-nu feedthrough Jacobian dy/du about the operating point.

📄Description

linmod returns the continuous-time state-space linearization of model about its post-INIT operating point.

The Jacobians are obtained by central finite differences of the same global right-hand side the ode4 / variable-step solver assembles: the continuous state x gathers every continuous block's state, the inputs u are the external-port Label Source blocks (isExternalPort), xdot = f(x, u) is the graph's derivative, and y the model's Label Sink outputs. A linear model linearizes to itself.

An input that should participate in B / D must be an external-port Label Source; a plain Label Source used for internal goto/from routing is not a model input.

Both top-level (flat) models and continuous states nested inside subsystems are supported: a nested state's coupling to the external inputs (B) and to the outputs across the subsystem boundary (C) is captured.

💡Examples

Linearize a first-order state-space model

d.blocks = { ...
  struct('id','u','type','labelSource','inputs',0,'outputs',1,'params',struct('label','u','isExternalPort',true)), ...
  struct('id','ss','type','stateSpace','inputs',1,'outputs',1,'params',struct('A',-2,'B',1,'C',1,'D',0)), ...
  struct('id','y','type','labelSink','inputs',1,'outputs',0,'params',struct('label','y')), ...
  struct('id','sc','type','scope','inputs',1,'outputs',0,'params',struct()) };
d.connections = { ...
  struct('from','u','to','ss','fromIndex',0,'toIndex',0), ...
  struct('from','ss','to','y','fromIndex',0,'toIndex',0), ...
  struct('from','ss','to','sc','fromIndex',0,'toIndex',0) };
f = [tempdir(), 'linmod_demo.nflow'];
fid = fopen(f,'wt'); fwrite(fid, jsonencode(d)); fclose(fid);
[A, B, C, D] = linmod(f)  % A = -2, B = 1, C = 1, D = 0