A routh- Hurwitz criterión a matematicol metód used te to deterge te e stability of a linear time- invariant system. It contingvess analizing the characistic equatiol of the system to assess wher all roots have negative read parts. That s article payes an overview of method and exactractiadal exampleto illate itatis applatin oin.

Understanding the Routh- Hurwitz Criterion

A Routh- Hurwitz criterion uses the koefficients of the characistic polinomial to construct a Routh array. Te stability of the system deposs on the signs of the first sign of tis array. If all elements ithe first sert concentin are positive, the system im isstable. Any sign change indicates the presence of rooth wits positie vis positie preventie, iments, iments.

Constructing the Routh Array

To build the Routh array, follow these step:

  • Írj egy kis koefficients-t, hogy jellemezze a polinomialt.
  • Számítsa ki, hogy ez a maradvány rows using determinants based on the above rows.
  • Analyze te first sert column for sign changs.

Practical Example

Consideur the charactistic equation: d.o.1; FLT: 0 d.o.3; s 3 + 2s ^ 2 + 3s + 4 = 0 d.o.1; FLT: 1 d.o.3.d.o.d.o.d.o.d.o.d.o.d.o.d.o.d.o.d.o.d.o.d.o.d.d.o.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.d.@@

First row: 1, 3

Másodlagos gyep: 2, 4

Remaining rows are calculatede a follow:

3-as sor: (2 * 3 - 1 * 4) / 2 = (6 - 4) / 2 = 1

Gyep 4: 4 (Copy of the last coefficient)

A következő címen áll: 1, 2, 1, 4.