Liu, Liu, and Liu, in the paper “A novel three-dimensional autonomous chaos system, Chaos, Solitons and Fractals. 39 (2009) 1950-1958”, introduce a novel three-dimensional autonomous chaotic system. In this paper, the fractional-order case is considered. The lowest order for the system to remain chaotic is found via numerical simulation. Stability analysis of the fractional-order system is stud...

In this paper, the technique applicable to reduce a high-order system to a low-order system is presented. The methods used are Routh stability array (RSA) method and stability equation (SE) method to get the reduced model of systems. The application of the techniques is examined over SISO linear time invariant systems and extended to MIMO systems. The step response performance of the reduced mo...

This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry. The reduction of variational Runge–Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical fea...

— In this note, we have shown special case on Routh stability criterion, which is not discussed, in previous literature. This idea can be useful in computer science applications.

This chapter investigates the relationship between Routh symmetry reduction and time discretization for Lagrangian systems. Within the framework of discrete variational mechanics, a discrete Routh reduction theory is constructed for the case of abelian group actions, and extended to systems with constraints and non-conservative forcing or dissipation. Variational Runge–Kutta discretizations are...

It is shown that the Hurwitz determinants associated with a real polynomial of degree n can be obtained from minors of matrices having orders n/2 or (« —1)/2 according as n is even or odd. The method used is based on forming companion matrices of appropriate polynomials, and is extended to calculation of Routh arrays, Sturm sequences and to complex polynomials, thus providing a new formulation ...

Using Brouwer degree, we prove a more general version of the zero exclusion principle for families of polynomials and apply it to obtain very simple proofs of extensions of recent results on the Routh-Hurwitz and Schur-Cohn stability of families of polynomials. 1. Introduction It is well know that the problem of the stability of a linear diierence or differential system with constant coeecients...