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1.
Robust Stability of Polynomials: New Approach 总被引:1,自引:0,他引:1
N. E. Mastorakis 《Journal of Optimization Theory and Applications》1997,93(3):635-638
The problem of the robust stability of a Hurwitz polynomial which is the characteristic polynomial of a discrete-time linear time-invariant system is investigated. A new approach based on the Rouché theorem of classical complex analysis is adopted. An interesting sufficient condition for robust stability is derived. Three examples are included to support the theoretical result. 相似文献
2.
N. E. Mastorakis 《Journal of Optimization Theory and Applications》2000,104(1):165-174
The paper investigates the problem of the robust stability of Schur polynomials. Recently, a new approach based on the Rouche theorem of classical complex analysis has been adopted for the solution of this problem. In this paper, an improvement of the previous solution is presented. This is the optimum solution of the robust stability problem for Schur polynomials, which is obtained by solving a minimization problem and is better than other methods in robust stability literature. Three numerical examples are given to illustrate the proposed method. 相似文献
3.
Nikola Samardzija 《Journal of Differential Equations》1983,48(1):60-70
A geometrical approach is used to derive a generalized characteristic value problem for dynamic systems described by homogeneous polynomials. It is shown that a nonlinear homogeneous polynomial system possesses eigenvectors and eigenvalues, quantities normally associated with a linear system. These quantities are then employed in studying stability properties. The necessary and sufficient conditions for all forms of stabilities characteristic of a two-dimensional system are provided. This result, together with the classical theorem of Frommer, completes a stability analysis for a two-dimensional homogeneous polynomial system. 相似文献
4.
《Communications in Nonlinear Science & Numerical Simulation》2010,15(12):4114-4130
In this paper, we consider the synchronization problem via nonlinear observer design. A new exponential polynomial observer for a class of nonlinear oscillators is proposed, which is robust against output noises. A sufficient condition for synchronization is derived analytically with the help of Lyapunov stability theory. The proposed technique has been applied to synchronize chaotic systems (Rikitake and Rössler systems) by means of numerical simulation. 相似文献
5.
In this paper, we extend the Perron-Frobenius theorem for positive polynomial operators in Banach lattices. The result obtained
is applied to derive necessary and sufficient conditions for the stability of positive polynomial operators. Then we study
stability radii: complex, real and positive radii of positive polynomial operators and show that in this case the three radii
coincide and can be computed by a simple formula. Finally, a simple example is given to illustrate the obtained results. 相似文献
6.
The problem of robust stability of a singular time-delay system is investigated. A novel Lyapunov–Krasovskii functional (LKF) is introduced which is a singular-type complete quadratic Lyapunov–Krasovskii functional with polynomial parameters. Stability conditions are derived in the form of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and lower conservatism of the new proposed stability criterion. 相似文献
7.
A recent paper (Ref. 1) established a new approach to estimate the robust stability radius of a Schur polynomial. This note points out that the approach given in Ref. 1 is not correct and also gives a counterexample to the main result of Ref. 1. 相似文献
8.
本文对包括区间多项式族和菱形多项式族的一类多项式族的鲁棒稳定性进行了研究.我们给出并证明了其中几个可用有限检验来判断的多项式族的Hurwitz稳定的实例;同时举例说明了有限检验对所有这一类多项式族并不总是可行的. 相似文献
9.
10.
An important (some say, the major) reason for using feedback control is the presence of uncertain parameters which are a natural part of any real dynamical model. In this paper, we consider uncertain constant parameters in a time-invariant linear plant and announce some new results concerning robust compensator synthesis. Using the min-max principle, we derive necessary conditions for fixed-order linear robust controllers assuring asymptotic stability or relative stability. These necessary conditions are an extension of the Lagrange multiplier method. This is achieved using a cost function based on the inverse of the so-called critical constraint. We present both matrix and polynomial versions; the latter allows controllers of fixed structure. We suggest a probability-one homotopy algorithm and solve some examples from the literature.The authors wish to thank Professor R. Bental, Faculty of Industrial Engineering at the Technion, for his suggestion to replace the cost function based on the inverse critical polynomial by a logarithmic function. 相似文献
11.
In this paper, we first consider the problem of determining the robust positivity of a real function f(x) as the real vector x varies over a box X∈Rl. We show that, it is sufficient to check a finite number of specially constructed points. This is accomplished by using some results on sign-definite decomposition. We then apply this result to determine the robust Hurwitz stability of a family of complex polynomials whose coefficients are polynomial functions of the parameters of interest. We develop an eight polynomial vertex stability test that is a sufficient condition of Hurwitz stability of the family. This test reduces to Kharitonov’s well known result for the special case where the parameters are just the polynomial coefficients. In this case, the result is tight. This test can be recursively and modularly used to construct an approximation of arbitrary accuracy to the actual stabilizing set. The result is illustrated by examples. 相似文献
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13.
Stéphane Clain Raphaël Loubère Gaspar J. Machado 《Advances in Computational Mathematics》2018,44(2):571-607
We propose a new family of high order accurate finite volume schemes devoted to solve one-dimensional steady-state hyperbolic systems. High-accuracy (up to the sixth-order presently) is achieved thanks to polynomial reconstructions while stability is provided with an a posteriori MOOD method which controls the cell polynomial degree for eliminating non-physical oscillations in the vicinity of discontinuities. Such a procedure demands the determination of a detector chain to discriminate between troubled and valid cells, a cascade of polynomial degrees to be successively tested when oscillations are detected, and a parachute scheme corresponding to the last, viscous, and robust scheme of the cascade. Experimented on linear, Burgers’, and Euler equations, we demonstrate that the schemes manage to retrieve smooth solutions with optimal order of accuracy but also irregular solutions without spurious oscillations. 相似文献
14.
我们讨论辛算法的线性稳定性和非线性稳定性,从动力系统和计算的角度论述了研究辛算法的这两类稳定性问题的重要性,分析总结了相关重要结果.我们给出了解析方法的明确定义,证明了稳定函数是亚纯函数的解析辛方法是绝对线性稳定的.绝对线性稳定的辛方法既有解析方法(如Runge-Kutta辛方法),也有非解析方法(如基于常数变易公式对线性部分进行指数积分而对非线性部分使用其它数值积分的方法).我们特别回顾并讨论了R.I.McLachlan,S.K.Gray和S.Blanes,F.Casas,A.Murua等关于分裂算法的线性稳定性结果,如通过选取适当的稳定多项式函数构造具有最优线性稳定性的任意高阶分裂辛算法和高效共轭校正辛算法,这类经优化后的方法应用于诸如高振荡系统和波动方程等线性方程或者线性主导的弱非线性方程具有良好的数值稳定性.我们通过分析辛算法在保持椭圆平衡点的稳定性,能量面的指数长时间慢扩散和KAM不变环面的保持等三个方面阐述了辛算法的非线性稳定性,总结了相关已有结果.最后在向后误差分析基础上,基于一个自由度的非线性振子和同宿轨分析法讨论了辛算法的非线性稳定性,提出了一个新的非线性稳定性概念,目的是为辛算法提供一个实际可用的非线性稳定性判别法. 相似文献
15.
A Fibonacci–Hessenberg matrix with Fibonacci polynomial determinant is referred to as a polynomial Fibonacci–Hessenberg matrix. Several classes of polynomial Fibonacci–Hessenberg matrices are introduced. The notion of two-dimensional Fibonacci polynomial array is introduced and three classes of polynomial Fibonacci–Hessenberg matrices satisfying this property are given. 相似文献
16.
Given a polynomial P in several variables over an algebraically closed field, we show that except in some special cases that we fully describe, if one coefficient is allowed to vary, then the polynomial is irreducible for all but at most deg(P)2 ? 1 values of the coefficient. We more generally handle the situation where several specified coefficients vary. 相似文献
17.
Sergio Blanes Fernando Casas Ander Murua 《Foundations of Computational Mathematics》2008,8(3):357-393
A comprehensive linear stability analysis of splitting methods is carried out by means of a 2×2 matrix K(x) with polynomial entries (the stability matrix) and the stability polynomial p(x) (the trace of K(x) divided by two). An algorithm is provided for determining the coefficients of all possible time-reversible splitting schemes
for a prescribed stability polynomial. It is shown that p(x) carries essentially all the information needed to construct processed splitting methods for numerically approximating the
evolution of linear systems. By conveniently selecting the stability polynomial, new integrators with processing for linear
equations are built which are orders of magnitude more efficient than other algorithms previously available.
This paper is dedicated to Arieh Iserles on the occasion of his 60th anniversary. 相似文献
18.
Lassi Paunonen 《Journal of Functional Analysis》2012,263(9):2555-2583
In this paper we study the robustness properties of strong and polynomial stability of semigroups of operators. We show that polynomial stability of a semigroup is robust with respect to a large and easily identifiable class of perturbations to its infinitesimal generator. The presented results apply to general polynomially stable semigroups and bounded perturbations. The conditions on the perturbations generalize well-known criteria for the preservation of exponential stability of semigroups. We also show that the general results can be improved if the perturbation is of finite rank or if the semigroup is generated by a Riesz-spectral operator. The theory is applied to deriving concrete conditions for the preservation of stability of a strongly stabilized one-dimensional wave equation. 相似文献
19.
The Cauchy problem for the (2+1)-dimensional nonlinear Boiti-Leon-Pempinelli (BLP) equation is studied within the framework of the inverse problem method. Evolution equations generated by the system of BLP equations under study are derived for the resolvent, Jost solutions, and scattering data for the two-dimensional Klein-Gordon differential operator with variable coefficients. Additional conditions on the scattering data that ensure the stability of the solutions to the Cauchy problem are revealed. A recurrence procedure is suggested for constructing the polynomial integrals of motion and the generating function for these integrals in terms of the spectral data.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 2, pp. 163–174, November, 1996. 相似文献
20.
For a class of smooth nonlinear multivariable systems whose working-points vary with time and the future working-points knowledge are unknown, a combination of a local linearization and a polytopic uncertain linear parameter-varying (LPV) state-space model is built to approximate the present and the future system’s nonlinear behavior, respectively. The combination models are constructed on the basis of a matrix polynomial multi-input multi-output (MIMO) RBF-ARX model identified offline for representing the underlying nonlinear system. A min–max robust MPC strategy is designed to achieve the systems’ output-tracking control based on the approximate models proposed. The closed loop stability of the MPC algorithm is guaranteed by the use of time-varying parameter-dependent Lyapunov function and the feasibility of the linear matrix inequalities (LMIs). The effectiveness of the modeling and control methods proposed in this paper is illustrated by a case study of a thermal power plant simulator. 相似文献