why lsim return empty states?

I have build a sparse state space system, and solved using lsim. According to the documentation, the third output represent the state trajectory.

When I run this example, the third output is empty.

Is there anything wrong I am doing? how can I get the states with time?

Thanks!

% inputs defining sparse state space system size
N_inputs = 41;
N_outputs = 240;
N_states = 2400;
N_time_steps = 10;

% defining the sparse state space system
G = sprand(N_states, N_states, 0.01);
B = sprand(N_states, N_inputs, 0.01);
E = sprand(N_outputs, N_states, 0.01);
D = 0;
C = sprand(N_states, N_states, 0.01);

sys = sparss(G, B, E, D, C);

% solving
t = linspace(0,1,N_time_steps);
[y,tOut,x] = lsim( ...
    sys, ...
    rand(N_inputs, length(t)), ...
    t);

% check the size of each output
disp(size(y))

    10   240

disp(size(tOut))

    10     1

disp(size(x)) % why this is empty? how can I force lsim to return it?

     0     0

Answer 1

[Paul]

According to the lsim doc page, the output x is returned when the input sys is a state-space model. The doc page further distinguishes between the input sys being a sparss model and an ss model. So I think that state trajectories are just returned as empty for sparss input. You can also see a comment that says exactly this if you drill down far enough into lsim in the debugger.

dbtype(fullfile(matlabroot,'toolbox/shared/controllib/engine/+ltipack/@spssdata/lsim.m'),'1:8')

1     function [y,x] = lsim(D,u,t,x0,~)
2     % Linear response simulation of state-space model with real coefficients.
3     % RE: Assume U is Ns x Nu and T has Ns samples.
4     
5     %	 Author: P. Gahinet
6     %   Copyright 2020 The MathWorks, Inc.
7     [ny,nu] = iosize(D);
8     x = [];   % never compute X for sparse

In theory, at least, we can augment the output equation to include the states.

rng(100)
N_inputs = 41;
N_outputs = 240;
N_states = 2400;
N_time_steps = 10;
% defining the sparse state space system
G = sprand(N_states, N_states, 0.01);
B = sprand(N_states, N_inputs, 0.01);
E = sprand(N_outputs, N_states, 0.01);
D = 0;
C = sprand(N_states, N_states, 0.01);

% augment
E = [E; sparse(eye(N_states))];


sys = sparss(G, B, E, D, C);

% solving
t = linspace(0,1,N_time_steps);
[y,tOut,x] = lsim( ...
    sys, ...
    rand(N_inputs, length(t)), ...
    t);


% collect states and outputs
x = y(:,N_outputs+1:end);
y = y(:,1:N_outputs);
size(y)

ans = 1×2

10 240

size(x)

ans = 1×2

10 2400

[Mahmoud Elzouka]

Thanks!

I wish matlab write in the docs at the output `x` that it will be empty is the system is sparse.

[Paul]

The doc could definitely be more clear in this regard. If you feel motivated, you can click on a star rating at the bottom of the doc page, after which I think that a window will pop-up where you can provide feedback to the doc writers.