Analysis and design of discrete-time linear systems with nested actuator saturations

Abstract This paper is concerned with the analysis and design of discrete-time linear systems subject to nested saturation functions. By utilizing a new compact convex hull representation of the saturation nonlinearity, a linear matrix inequalities (LMIs) based condition is obtained for testing the local and global stability of the considered nonlinear system. The estimation of the domain of attraction and the design of feedback gains such that the estimation of the domain of attraction for the resulting closed-loop system is maximized are then converted into some LMIs based optimization problems. Compared with the existing results on the same problems, the proposed solutions are less conservative as more slack variables are introduced into the conditions. A couple of numerical examples are worked out to validate the effectiveness of the proposed approach.

[1]  Eduardo F. Camacho,et al.  Estimation of the domain of attraction for saturated discrete-time systems , 2006, Int. J. Syst. Sci..

[2]  Sophie Tarbouriech,et al.  Stability and Stabilization of Linear Systems with Saturating Actuators , 2011 .

[3]  Weiyao Lan,et al.  Semiglobal stabilization and output regulation of singular linear systems with input saturation , 2003, IEEE Trans. Autom. Control..

[4]  Sophie Tarbouriech,et al.  Local stabilization of discrete-time linear systems with saturating controls: an LMI-based approach , 2001, IEEE Trans. Autom. Control..

[5]  Zongli Lin,et al.  An analysis and design method for discrete-time linear systems under nested saturation , 2002, IEEE Trans. Autom. Control..

[6]  Zongli Lin,et al.  An analysis and design method for linear systems under nested saturation , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[7]  Luca Zaccarian,et al.  Linear LMI-based external anti-windup augmentation for stable linear systems , 2004, Autom..

[8]  Karolos M. Grigoriadis,et al.  Anti-windup controller synthesis via linear parameter-varying control design methods , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[9]  Sophie Tarbouriech,et al.  Local stabilization of linear systems under amplitude and rate saturating actuators , 2003, IEEE Trans. Autom. Control..

[10]  Guang-Ren Duan,et al.  An improved treatment of saturation nonlinearity with its application to control of systems subject to nested saturation , 2011, Autom..

[11]  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).

[12]  Tingshu Hu,et al.  Composite quadratic Lyapunov functions for constrained control systems , 2003, IEEE Trans. Autom. Control..

[13]  David G. Ward,et al.  Anti-windup design of output tracking systems subject to actuator saturation and constant disturbances , 2004, Autom..

[14]  Tingshu Hu,et al.  Exact characterization of invariant ellipsoids for single input linear systems subject to actuator saturation , 2002, IEEE Trans. Autom. Control..

[15]  Sophie Tarbouriech,et al.  Stability analysis and stabilization of systems presenting nested saturations , 2006, IEEE Transactions on Automatic Control.

[16]  Jiri Matousek,et al.  Lectures on discrete geometry , 2002, Graduate texts in mathematics.

[17]  Guang-Ren Duan,et al.  Global and Semi-Global Stabilization of Linear Systems With Multiple Delays and Saturations in the Input , 2010, SIAM J. Control. Optim..

[18]  Luca Zaccarian,et al.  Piecewise-quadratic Lyapunov functions for systems with deadzones or saturations , 2009, Syst. Control. Lett..

[19]  Jordan M. Berg,et al.  An analysis of the destabilizing effect of daisy chained rate-limited actuators , 1996, IEEE Trans. Control. Syst. Technol..

[20]  Guang-Ren Duan,et al.  A novel nested non-linear feedback law for global stabilisation of linear systems with bounded controls , 2008, Int. J. Control.

[21]  Eduardo Sontag,et al.  Global stabilization of linear discrete-time systems with bounded feedback , 1997 .

[22]  James Lam,et al.  Saturated linear quadratic regulation of uncertain linear systems: Stability region estimation and controller design , 2002 .

[23]  Tong Heng Lee,et al.  Composite nonlinear feedback control for linear systems with input saturation: theory and an application , 2003, IEEE Trans. Autom. Control..

[24]  Jie Huang,et al.  Semi-global stabilization of singular linear systems with input saturation , 2003, Proceedings of the 2003 IEEE International Symposium on Intelligent Control.

[25]  Fen Wu,et al.  Output feedback control of saturated discrete-time linear systems using parameter-dependent Lyapunov functions , 2008, Syst. Control. Lett..

[26]  Zongli Lin,et al.  Stabilization of linear systems with input delay and saturation—A parametric Lyapunov equation approach , 2010 .

[27]  Eduardo Sontag,et al.  A general result on the stabilization of linear systems using bounded controls , 1994, IEEE Trans. Autom. Control..

[28]  A. Teel.  Semi-global stabilizability of linear null controllable systems with input nonlinearities , 1995, IEEE Trans. Autom. Control..

[29]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[30]  Zongli Lin,et al.  Semi-global Exponential Stabilization of Linear Systems Subject to \input Saturation" via Linear Feedbacks , 1993 .

[31]  T. Alamo,et al.  Improved computation of ellipsoidal invariant sets for saturated control systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.