linearize
Linearize an explicit multilinear model around an operating point
Contents
Syntax
linearize(msys,x,u)
Description
linearize(msys,x,u) Linearizes an explicit MTI state-space model of type mss around an operating point of the states, given by the scalar or vector x, and the inputs, provided by the scalar or vector u. The linearization is done by computing the Jacobian, which was shown for explicit MTI models stored as a norm-1 CP-decomposed tensor in [1]. If no output equation of the mss object is specified, all states are outputs and feedthrough is set to zero.
Input Arguments
msys: multilinear MTI model, mss object
x : state operating point, vector
u : input operating point, vector
Output Arguments
linSs: linear LTI model, ss object
Example:
Second-order explicit MTI model with 2 states and 1 input (expanded and factored form)
.
The factored explicit MTI model as CPN1 object thus has a structure matrix
S = [0.5 -0.5; 1 0; 0 1];
and the parameter matrix
phi = [2 0; 4 6];
Then we can create explicit MTI model as a CPN1 object and the mss-object
tens = CPN1(S,phi); msys = mss(tens);
and assume the operating point for the states x and the input u
x_op = [-1;1]; u_op = 3;
Then we can linearize the explicit MTI model
lsys = linearize(msys,x_op,u_op)
Warning: No Outputs defined, assuming states as outputs. lsys = A = x1 x2 x1 1 0 x2 -7 0 B = u1 x1 0 x2 6 C = x1 x2 y1 1 0 y2 0 1 D = u1 y1 0 y2 0 Continuous-time state-space model.
You can find a full example here: open linearization example
References
[1] C. Kaufmann, D. Crespí, G. Lichtenberg, G. Pangalos, and C. Cateriano Yáñez, "Efficient Linearization of Explicit Multilinear Systems using Normalized Decomposed Tensors," IFAC-PapersOnLine, vol. 56, no. 2, pp. 7312–7317, Jan. 2023, doi: https://doi.org/10.1016/j.ifacol.2023.10.344.