Get chain of integrators LTI System
============================================================================
Get an n-d discrete chain of integrators in the form of an LtiSystem object
given a discretization time-step T.
Chain of integrators model:
x_{k+1} = A * x_{k} + B * u_{k} + w_{k}
A = [1, T, T^2/2, ... T^n/n!;
0, 1, T, ... T^(n-1)/(n-1)!;
...
0, 0, ... ... T;
0, 0, ... ... 1];
B = [T^n/n!;
T^(n-1)/(n-1)!
...
T];
Usage:
------
% 3-d chain of integrators with U = [-1,1] and no (empty) disturbance
sys = getChainOfIntegLtiSystem(3, 0.2, ...
'InputSpace', Polyhedron('lb', -1, 'ub', 1));
============================================================================
sys = getChainOfIntegLtiSystem(dim, T, input_space, disturb)
Inputs:
-------
dim - Dimensions
T - Discretization time step
input_space - Input space (Polyhedron)
disturb - Disturbance object (Polyhedron / RandomVector / empty)
Outputs:
--------
sys - LtiSystem object describing the chain of integrators
=============================================================================
This function is part of the Stochastic Reachability Toolbox.
License for the use of this function is given in
https://sreachtools.github.io/license/