Abstract
A new criterion for Schur stability is derived by using basic results of the theory of orthogonal polynomials. In particular, we use the relation between orthogonal polynomials on the real line and on the unit circle known as the Szegő transformation. Some examples are presented.
Highlights
The stability problem of dynamical systems is of great interest because of its numerous applications, mainly in control systems
It is well known that for time-invariant linear dynamical systems, stability is determined by the roots of a characteristic equation that has a polynomial form
Another topic that has been studied consists of verifying the Schur stability property by considering uncertainty in the polynomial coefficients, which is known as robust Schur stability
Summary
The stability problem of dynamical systems is of great interest because of its numerous applications, mainly in control systems. Another topic that has been studied consists of verifying the Schur stability property by considering uncertainty in the polynomial coefficients, which is known as robust Schur stability. The Schur stability property of polynomials depends directly on their coefficients, it is possible to define regions in the coefficient space for which the polynomial meets the condition of Schur stability These regions are generally represented by semi-algebraic sets, which in turn, makes it possible to use criteria such as the Jury test. In this paper we present a new criterion to verify the Schur stability property This is derived by using the relation between orthogonal polynomials on the real line and on the unit circle known as the Szegő transformation.
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