Inners and Stability of Dynamic Systems

Jury, E.I.; Paynter, H. M.

doi:10.1115/1.3426906

Cited by 60 publications

(77 citation statements)

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“…The solution (30), (31) is asymptotically stable if and only if the roots Λ 1 , Λ 2 of the characteristic equation of the stability matrix [s ij ], X 2 + αX + β, fulfill inequalities Λ 1,2 < 1. Using the Jury stability test which is a convenient implementation of the Schur-Cohn criterion [49],…”

Section: Case (Iii): T I ∈ (0 H) T J ∈ (H 1)mentioning

confidence: 99%

Dynamics of impacts with a table moving with piecewise constant velocity

Okniński

Radziszewski

2009

Nonlinear Dyn

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Dynamics of a ball moving in gravitational field and colliding with a moving table is considered. The motion of the limiter is assumed as periodic with piecewise constant velocity. It is assumed that the table moves up with a constant velocity and then goes down with another constant velocity. The Poincaré map describing evolution from an impact to the next impact is derived. Several classes of solutions are computed in analytical form.

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Section: Case (Iii): T I ∈ (0 H) T J ∈ (H 1)mentioning

confidence: 99%

Dynamics of impacts with a table moving with piecewise constant velocity

Okniński

Radziszewski

2009

Nonlinear Dyn

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“…n ) 2 < 0, and |D 0 (z)| = | D 0 (z)| when |z| = 1, we have that, when |z| = 1, |a (1) 0 D 0 (z)| < |a (1) n D 0 (z)|. Choose P (z) = −a (1) n D 0 (z), Q(z) = a (1) 0 D 0 (z).…”

Section: Sincementioning

confidence: 99%

“…In his breakthrough paper, Jury [1], developed a scheme that can be used to determine whether or not the moduli of all roots of a real coefficient polynomial are less than 1 and the criterion has been used widely in the stability analysis in discrete dynamic systems. In both the dynamic system theory and its practical applications, people try to find out not only when the system is stable and when it is not, but also the critical states between stable and unstable ones [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Extended Jury criterion

2010

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In this paper, algebraic criteria are established to determine whether or not a real coefficient polynomial has one or two pairs of conjugate complex roots whose moduli are equal to 1 and the other roots have moduli less than 1 directly from its coefficients. The form and the function of the criteria are similar to those of the Jury criterion which can be used to determine whether or not all the moduli of the roots of a real coefficient polynomial are less than 1.

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“…As noted in Section 3, the sufficiency of Corollary 5.3 can also be proved by using the quadratic Lyapunov function (13) proposed in [8], [23].…”

Section: Corollary 52 For the Asymptotic Stability Of The System (2mentioning

confidence: 99%

“…(see, e.g. [13] and the references therein). In the present paper, we consider the following linear shift-invariant discrete systems described by the equations     …”

Section: Introductionmentioning

confidence: 99%

Asymptotic Stability of a Class of Linear Discrete Systems with Multiple Independent Variables

Liu

Molchanov

2003

Circuits Syst Signal Process

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This paper investigates the problem of asymptotic stability for a class of linear shift-invariant discrete systems with multiple independent variables. We establish the equivalence of this problem and that of robust stability for a class of ordinary linear shiftvarying discrete systems with the matrix uncertainty set defined by the coefficient matrices of the original system. On the basis of this equivalence, by using the variational method and Lyapunov's second method, necessary and sufficient conditions for asymptotic stability are obtained in different forms for the class of systems considered. The parametric classes of Lyapunov functions which define the necessary and sufficient conditions of asymptotic stability are determined. We use the piecewise linear polyhedral Lyapunov functions of the infinity vector norm type to derive an algebraic criterion for asymptotic stability of the given class of discrete systems in the form of solvability conditions of a set of matrix equations. A simple sufficient condition of asymptotic stability is also obtained which becomes necessary and sufficient for several special cases of the discrete systems under consideration.

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Inners and Stability of Dynamic Systems

Cited by 60 publications

References 0 publications

Dynamics of impacts with a table moving with piecewise constant velocity

Dynamics of impacts with a table moving with piecewise constant velocity

Extended Jury criterion

Asymptotic Stability of a Class of Linear Discrete Systems with Multiple Independent Variables

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