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On stable cones of polynomials via reduced Routh parameters

Ülo Nurges;  Juri Belikov;  Igor Artemchuk — 2016

Kybernetika

A problem of inner convex approximation of a stability domain for continuous-time linear systems is addressed in the paper. A constructive procedure for generating stable cones in the polynomial coefficient space is explained. The main idea is based on a construction of so-called Routh stable line segments (half-lines) starting from a given stable point. These lines (Routh rays) represent edges of the corresponding Routh subcones that form (possibly after truncation) a polyhedral (truncated) Routh...

State-space realization of nonlinear control systems: unification and extension via pseudo-linear algebra

Juri Belikov;  Ülle Kotta;  Maris Tõnso — 2012

Kybernetika

In this paper the tools of pseudo-linear algebra are applied to the realization problem, allowing to unify the study of the continuous- and discrete-time nonlinear control systems under a single algebraic framework. The realization of nonlinear input-output equation, defined in terms of the pseudo-linear operator, in the classical state-space form is addressed by the polynomial approach in which the system is described by two polynomials from the non-commutative ring of skew polynomials. This allows...

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