rmss

Utility function.

Generate a random multilinear state-space (mss) model.

Source: src/rmss.m

Overview

rmss builds a random explicit multilinear state-space model of a requested size — n states, m inputs, p outputs and rank r — handy for tests, examples and scaling benchmarks. The result is a continuous-time mss by default, or a discrete-time one when a positive time step is given (the former drmss).

The model tensor is drawn and assembled by CPNTensor.randCpn; rmss wraps it in an mss with the matching index vectors.

Description

The model is a rank-2r CPNTensor wrapped as an mss, laid out in a fixed order:

Rows / columns	Assignment
structure rows `1..n`	states $x_1,\dots,x_n$
structure rows `n+1..n+m`	inputs $u_1,\dots,u_m$
parameter rows `1..n`	state equations $\delta x_i$
parameter rows `n+1..n+p`	output equations $y_i$
columns `1..r`	state-equation monomials
columns `r+1..2r`	output-equation monomials

The state and output equations get separate monomials — the output block is given its own structure rather than reusing the state monomials — so the model carries a full output structure. See CPNTensor.randCpn for the tensor layout, the per-block sparsity and the size rationale behind it.

The model is in the monomial base with no False factors: structure entries equal to 1 are True and every other nonzero is Continuous.

For a fixed rng seed the model is reproducible.

Input arguments

Argument	Description
`n`	Number of states. Defaults to a positive random integer, `max(1, round(abs(10*randn)))`.
`m`	Number of inputs. Default `1`.
`p`	Number of outputs. Default `1`.
`r`	Rank of each equation block; the model tensor has rank `2r`. Default `round((n+m)/2)`.
`ts`	Time step size. Default `0` (continuous-time). `ts > 0` gives a discrete-time model.

Note the argument order n, m, p, r, ts here — the number of inputs m comes before the number of outputs p, the opposite of CPNTensor.randCpn.

Output arguments

Output	Description
`msys`	Random `mss` model of the requested size.

Syntax

msys = rmss(n)
msys = rmss(n, m, p)
msys = rmss(n, m, p, r)
msys = rmss(n, m, p, r, ts)

A continuous-time model

% n=4 states, m=1 input, p=1 output, rank r=6
msys = rmss(4, 1, 1, 6);

A discrete-time model

% same size, sampled at ts = 0.1
msys = rmss(4, 1, 1, 6, 0.1);