The Routh and Routh‐Hurwitz Stability Criteria

1962 ◽  
Vol 34 (1) ◽  
pp. 25-27 ◽  
Author(s):  
J. Morris
Keyword(s):  
Stability Criteria ◽  
Hurwitz Stability

scholarly journals Mathematical Modelling of Deforestation Due to Population Density and Industrialization

Jurnal Varian ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 9-16
Author(s):  
Didiharyono D. ◽  
Irwan Kasse
Keyword(s):  
Numerical Simulation ◽  
Population Density ◽  
Mathematical Modelling ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Stability Criteria ◽  
Hurwitz Stability ◽  
Stable Conditions ◽  
Linear Differential ◽  
The Stability

The focus of the study in this paper is to model deforestation due to population density and industrialization. To begin with, it is formulated into a mathematical modelling which is a system of non-linear differential equations. Then, analyze the stability of the system based on the Routh-Hurwitz stability criteria. Furthermore, a numerical simulation is performed to determine the shift of a system. The results of the analysis to shown that there are seven non-negative equilibrium points, which in general consist equilibrium point of disturbance-free and equilibrium points of disturbances. Equilibrium point TE7(x, y, z) analyzed to shown asymptotically stable conditions based on the Routh-Hurwitz stability criteria. The numerical simulation results show that if the stability conditions of a system have been met, the system movement always occurs around the equilibrium point.

On a Specialised Case of the Routh-Hurwitz Stability Criteria

1968 ◽  
Vol 19 (4) ◽  
pp. 352-356 ◽  
Author(s):  
E. Nissim
Keyword(s):  
The State ◽  
Stability Test ◽  
Characteristic Polynomials ◽  
Stability Criteria ◽  
Test Functions ◽  
Characteristic Equations ◽  
Hurwitz Stability ◽  
The Stability ◽  
Complex Coefficients

SummaryThe well-known Routh-Hurwitz stability criteria apply to polynomial characteristic equations with real coefficients. Lesser known criteria were devised by Hurwitz for the case of polynomials with complex coefficients. However, when polynomials with real coefficients and even powers only are directly subjected to the first-mentioned criteria, all the test determinants obtained vanish identically and thus fail to indicate the state of stability. In the present paper, the stability test functions for such characteristic polynomials are derived.

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