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Control System for an Object with Interval-Given Parameters: Quality Analysis Based on Leading Coefficients of Characteristic Polynomials

Yury Chursin(1*), Dmitry Sonkin(2), Mikhail Sukhodoev(3), Ruslan Nurmuhametov(4), Vsevolod Pavlichev(5)

(1) Tomsk Polytechnic University, Russian Federation
(2) Tomsk Polytechnic University, Russian Federation
(3) Tomsk Polytechnic University, Russian Federation
(4) Tomsk Polytechnic University, Russian Federation
(5) Tomsk Polytechnic University, Russian Federation
(*) Corresponding author



This paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust control system based on leading coefficients of characteristic polynomials. The problem of determining quality indices of a system, which characteristic polynomials are with interval coefficients, is one of the relevant ones in the robust control theory. This article deals with the interval characteristic polynomial coefficients of a control system. Based on the extended root locus method, we have determined conditions, at which the vertices of a polyhedron of coefficients will be mapped onto root domain. The root analysis carried out by us showed the conditions for achieving the minimum degree of stability of the system under consideration, as well as the maximum degree of oscillation. Thus, the paper describes the design of a method intended for finding the control leading coefficients of polynomials that will allow analyzing the minimum stability degree and the maximum oscillativity degree of control systems for objects with interval-given parameters. A complete solution to a problem of the system control is given. Thus, the stability conditions of the system are described in full.
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Characteristic Polynomial; Interval Coefficients; Root Locus; Root Localization; Parameterized Polyhedron Vertices; Stability Degree; Oscillativity Degree; Phase Equation; Angle of Leaving

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