New stability conditions via reflection coefficients of polynomials

The geometry of stable discrete polynomials using their coefficients and reflection coefficients is investigated. Starting from so-called barycentric simplex some necessary stability conditions in terms of unions of polytopes are obtained by splitting the unit hypercube of reflection coefficients. Sufficient stability conditions in terms of linear covers of reflection vectors of a family of stable polynomials improve the Cohn stability criterion.

[1]  Dimitri Peaucelle,et al.  Ellipsoidal approximation of the stability domain of a polynomial , 2001, 2001 European Control Conference (ECC).

[2]  Suguru Arimoto,et al.  Selective learning with a forgetting factor for robotic motion control , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[3]  Huang Lin,et al.  Root locations of an entire polytope of polynomials: It suffices to check the edges , 1987, 1987 American Control Conference.

[4]  Jürgen Ackermann,et al.  Sampled-Data Control Systems , 1985 .

[5]  Prashant Batra,et al.  On necessary conditions for real robust Schur-stability , 2003, IEEE Trans. Autom. Control..

[6]  Toshiharu Sugie,et al.  An iterative learning control law for dynamical systems , 1991, Autom..

[7]  B. R. Barmish,et al.  A survey of extreme point results for robustness of control systems, , 1993, Autom..

[8]  James S. Meditch,et al.  A canonical parameter space for linear systems design , 1978 .

[9]  B. Porter,et al.  Iterative learning control of partially irregular multivariable plants with initial impulsive action , 1991 .

[10]  ASYMPTOTIC STABILITY OF AN EQUILIBRIUM P . OSITION OF A FAMILY OF SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS , 2022 .

[11]  E. Jury.  ROBUSTNESS OF DISCRETE SYSTEMS: A REVIEW , 1990 .

[12]  Shankar P. Bhattacharyya,et al.  Elementary proofs of some classical stability criteria , 1990 .

[13]  L. Jetto.  Strong stabilization over polytopes , 1999, IEEE Trans. Autom. Control..

[14]  J. Ackermann,et al.  Robust control , 2002 .

[15]  Andrew Bartlett,et al.  Robust Control: Systems with Uncertain Physical Parameters , 1993 .

[16]  Shankar P. Bhattacharyya,et al.  Robust Control: The Parametric Approach , 1994 .

[17]  Giuseppe Cala.  Ellipsoidal bounds for uncertain linear equations and dynamical systems , 2004 .

[18]  Domingo Docampo,et al.  Extreme-point robust stability results for discrete-time polynomials , 1994, IEEE Trans. Autom. Control..

[19]  Q. I. Rahman,et al.  Analytic theory of polynomials , 2002 .

[20]  B. Paden,et al.  Stability of learning control with disturbances and uncertain initial conditions , 1992 .

[21]  Christopher V. Hollot,et al.  Some discrete-time counterparts to Kharitonov's stability criterion for uncertain systems , 1986 .

[22]  Zhihua Qu.  Robust control of nonlinear systems by estimating time variant uncertainties , 2002, IEEE Trans. Autom. Control..

[23]  Alan V. Oppenheim,et al.  Discrete-time Signal Processing. Vol.2 , 2001 .

[24]  J. Ackermann.  Sampled-Data Control Systems: Analysis and Synthesis, Robust System Design , 1985 .

[25]  Francesco Amato,et al.  An Algorithm to Cover the Image of a Function with a Polytope: Applications to Robust Stability Problems , 1993 .

[26]  Mingxuan Sun,et al.  An iterative learning controller with initial state learning , 1999, IEEE Trans. Autom. Control..

[27]  B. O. Anderson,et al.  Robust Schur polynomial stability and Kharitonov's theorem , 1987, 26th IEEE Conference on Decision and Control.

[28]  R. Luus,et al.  Discrete Kharitonov's theorem and robust control , 2002 .

[29]  Richard Greiner,et al.  Necessary conditions for Schur-stability of interval polynomials , 2004, IEEE Transactions on Automatic Control.

[30]  B. Porter,et al.  Iterative learning control of partially irregular multivariable plants with initial state shifting , 1991 .

[31]  Ennu Riistern.  THE DISTANCE FROM STABILITY BOUNDARY AND REFLECTION VECTORS , 2002 .