Interval Frazer-Duncan criterion for stability analysis of linear systems with dependent coefficients in the characteristic polynomial
نویسندگان
چکیده
The paper addresses the stability analysis of linear continuous systems under interval uncertainties. A new implementation of the interval Frazer-Duncan criterion is suggested to estimate the stability of the system considered. It is based on obtaining the interval extensions of the coefficients 0 a and n a in the characteristic polynomial as well as the determinant 1 − ∆ n from the Hurwitz matrix. In general, each of them is nonlinear function of independent system parameters. The interval extensions studied are determined by using modified affine arithmetic. Two sufficient conditions on stability and instability of the linear system considered are obtained. Numerical example illustrating the applicability of the method suggested is solved in the end of the paper. Key-Words: Robust stability analysis of linear systems, Interval Frazer-Duncan criterion, Interval extension, Affine arithmetic.
منابع مشابه
Delay-Dependent Robust Asymptotically Stable for Linear Time Variant Systems
In this paper, the problem of delay dependent robust asymptotically stable for uncertain linear time-variant system with multiple delays is investigated. A new delay-dependent stability sufficient condition is given by using the Lyapunov method, linear matrix inequality (LMI), parameterized first-order model transformation technique and transformation of the interval uncertainty in to the norm ...
متن کاملStability Analysis of Polynomials with Polynomic Uncertainty
When dealing with systems with parameter uncertainty most attention is paid to robustness analysis of linear time-invariant systems. In literature the most often investigated topic of analysis of linear time-invariant systems with parametric uncertainty is the problem of stability analysis of polynomials whose coefficients depend on uncertain parameters. The aim is to verify that all roots of s...
متن کاملRoot Distribution and Stability Analysis of Two Dimensional Linear Discrete Systems Using Sign Criterion with Real Coefficients
A new idea was proposed to find out the stability and root location of two dimensional linear time invariant discrete system (LTIDS) for real coefficient polynomials. For determining stability the sign criterion is synthesized from the jury’s method for stability which is derived from the characteristic polynomial coefficients of the discrete system. The number of roots lying inside or outside ...
متن کاملStability and numerical solution of time variant linear systems with delay in both the state and control
In this paper, stability for uncertain time variant linear systems with time delay is studied. A new sufficient condition for delay-dependent systems is given in matrix inequality form which depends on the range of delay. Then, we introduce a new direct computational method to solve delay systems. This method consists of reducing the delay problem to a set of algebraic equations by first expand...
متن کاملNumerical solution for the risk of transmission of some novel coronavirus (2019-nCov) models by the Newton-Taylor polynomial solutions
In this paper we consider two type of mathematical models for the novel coronavirus (2019-nCov), which are in the form of a nonlinear differential equations system. In the first model the contact rate, , and transition rate of symptomatic infected indeviduals to the quarantined infected class, , are constant. And in the second model these quantities are time dependent. These models are the...
متن کامل