Computing estimates of the region of attraction for rational control systems with saturating actuators

This study focuses on the problem of regional stability analysis of rational control systems with saturating actuators. Estimates of the region of attraction are computed by means of invariant domains associated to rational Lyapunov functions. Conditions for computing these invariant domains (regions of stability) are proposed in the form of linear matrix inequalities (LMIs). These conditions are derived considering a differential-algebraic representation of the rational system dynamics. The saturation effects are taken into account by means of a generalised sector condition for deadzone non-linearities. The obtained conditions are cast in convex optimisation schemes in order to compute a Lyapunov function which leads to a maximised estimate of the region of attraction.

[1]  A. Vicino,et al.  On the estimation of asymptotic stability regions: State of the art and new proposals , 1985 .

[2]  Mathukumalli Vidyasagar,et al.  Maximal lyapunov functions and domains of attraction for autonomous nonlinear systems , 1981, Autom..

[3]  J. Thorp,et al.  Stability regions of nonlinear dynamical systems: a constructive methodology , 1989 .

[4]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[5]  L. Ghaoui.  State-feedback control of rational systems using linear-fractional representations and LMIs , 1994 .

[6]  Gérard Scorletti,et al.  Control of rational systems using linear-fractional representations and linear matrix inequalities , 1996, Autom..

[7]  Wei-Min Lu,et al.  Nonlinear optimal control: alternatives to Hamilton-Jacobi equation , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[8]  Stephen P. Boyd,et al.  Analysis of linear systems with saturation using convex optimization , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[9]  Sophie Tarbouriech,et al.  LMI relaxations for robust stability of linear systems with saturating controls , 1999, Autom..

[10]  Tetsuya Iwasaki,et al.  On the use of multi-loop circle criterion for saturating control synthesis , 2000 .

[11]  Robert E. Skelton,et al.  Stability tests for constrained linear systems , 2001 .

[12]  Tingshu Hu,et al.  An analysis and design method for linear systems subject to actuator saturation and disturbance , 2002, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[13]  Daniel J. Pagano,et al.  Detection of attraction domains of non-linear systems using bifurcation analysis and Lyapunov functions , 2002 .

[14]  Minyue Fu,et al.  Guaranteed cost control of uncertain nonlinear systems via polynomial lyapunov functions , 2002, IEEE Trans. Autom. Control..

[15]  S. Tarbouriech,et al.  Anti-windup design with guaranteed regions of stability: an LMI-based approach , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[16]  Graziano Chesi.  Estimating the domain of attraction for uncertain polynomial systems , 2004, Autom..

[17]  A. S. e Silva,et al.  Stability analysis and control of a class of differential‐algebraic nonlinear systems , 2004 .

[18]  Sophie Tarbouriech,et al.  Antiwindup design with guaranteed regions of stability: an LMI-based approach , 2005, IEEE Transactions on Automatic Control.

[19]  A. Garulli,et al.  LMI‐based computation of optimal quadratic Lyapunov functions for odd polynomial systems , 2005 .

[20]  D.F. Coutinho,et al.  Piecewise Lyapunov Functions to the Stability Analysis of Rational Systems subject to Multiple State Constraints , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[21]  Luca Zaccarian,et al.  Stability and Performance for Saturated Systems via Quadratic and Nonquadratic Lyapunov Functions , 2006, IEEE Transactions on Automatic Control.

[22]  Eduardo F. Camacho,et al.  A new concept of invariance for saturated systems , 2006, Autom..

[23]  Graziano Chesi,et al.  On the Gap Between Positive Polynomials and SOS of Polynomials , 2007, IEEE Transactions on Automatic Control.

[24]  Graziano Chesi,et al.  Estimating the domain of attraction via union of continuous families of Lyapunov estimates , 2007, Syst. Control. Lett..

[25]  O. Hachicho,et al.  A novel LMI-based optimization algorithm for the guaranteed estimation of the domain of attraction using rational Lyapunov functions , 2007, J. Frankl. Inst..

[26]  Masayuki Sato,et al.  Comparison between SOS approach and Slack Variable approach for non-negativity check of polynomial functions: Multiple variable case , 2007, 2007 European Control Conference (ECC).

[27]  Isabelle Queinnec,et al.  Control design for a class of nonlinear continuous-time systems , 2008, Autom..

[28]  Minyue Fu,et al.  ℒ︁2‐Gain analysis and control of uncertain nonlinear systems with bounded disturbance inputs , 2008 .