determine whether a transfer function is stable in rust

To determine whether a transfer function is stable in Rust, you first need to define the transfer function, which can be represented as a rational polynomial.

One common method to determine stability is to look at the poles of the transfer function in the complex s-plane. If all the poles lie in the left-half of the s-plane, the system is stable. A pole is a value of s which makes the denominator of the transfer function to zero, thus making the transfer function go to infinity. If the poles lie in the right-half of the s-plane, the system is unstable. In this case, the system will exhibit exponential growth and will not converge to a steady-state value.

Here is a sample code in Rust that determines stability using the pole placement method:

main.rs
extern crate ndarray;
use ndarray::{Array, Ix2};

// define the transfer function polynomial
let num = Array::from(vec![1., 2., 1.]);   // numerator coefficients
let den = Array::from(vec![1., -0.2, 1.]); // denominator coefficients

// calculate the poles of the transfer function
let poles = den.roots().unwrap();

// check if the system is stable
let is_stable = poles.iter().all(|&p| p.real() < 0.0);

if is_stable {
    println!("The system is stable.");
} else {
    println!("The system is unstable.");
}
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In this code, we use the ndarray crate to define the transfer function polynomial as num and den. We can then calculate the poles of the transfer function using the roots method. Finally, we check if all the real parts of the poles are negative, which indicates stability.