Stability analysis of discrete-time quadratic periodically time-varying systems with input saturation

This paper proposes a novel approach to stability analysis for discrete-time quadratic periodically time-varying systems with input saturation. The concept of so-called periodic contractively invariant set is employed to analyze the open-loop stability or closed-loop stability. As a result, sufficient conditions for local stability and stabilization are derived in terms of linear matrix inequalities (LMIs) and LMIs-based optimization problems are then given to estimate the stability region of the corresponding systems. Finally, a simulation example is presented to illustrate the efficiency of the proposed technique.

[1]  Zongli Lin,et al.  Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation , 2003, IEEE Trans. Fuzzy Syst..

[2]  S. Bittanti,et al.  Analysis of discrete-time linear periodic systems , 1996 .

[3]  Carlos E. de Souza,et al.  Nonlinear control design for open-loop unstable quadratic discrete-time systems , 2011, 2011 9th IEEE International Conference on Control and Automation (ICCA).

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

[5]  Sophie Tarbouriech,et al.  State feedback design for input-saturating quadratic systems , 2010, Autom..

[6]  C. Cosentino,et al.  Stabilization of impulsive quadratic systems over polytopic sets , 2013 .

[7]  Francesco Amato,et al.  Sufficient Conditions for Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems , 2010, IEEE Transactions on Automatic Control.

[8]  E. Kamen,et al.  A transfer function approach to linear time-varying discrete-time systems , 1982, 1982 21st IEEE Conference on Decision and Control.

[9]  S. Bittanti,et al.  Periodic Systems: Filtering and Control , 2008 .

[10]  Carlos E. de Souza,et al.  Nonlinear State Feedback Design With a Guaranteed Stability Domain for Locally Stabilizable Unstable Quadratic Systems , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  Francesco Amato,et al.  Stability analysis of nonlinear quadratic systems via polyhedral Lyapunov functions , 2008, 2008 American Control Conference.

[12]  Guang-Ren Duan,et al.  Stability and stabilization of discrete-time periodic linear systems with actuator saturation , 2011, Autom..

[13]  Rafal Wisniewski,et al.  Satellite Attitude Control Using Only Electromagnetic Actuation , 1997 .

[14]  W. Marsden.  I and J , 2012 .

[15]  Carlo Cosentino,et al.  On the region of attraction of nonlinear quadratic systems , 2007, Autom..

[16]  W. Ukovich,et al.  Linear programming approach to the control of discrete-time periodic systems with uncertain inputs , 1993 .

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

[18]  Patrizio Colaneri,et al.  Invariant representations of discrete-time periodic systems , 2000, Autom..

[19]  Frank Allgöwer,et al.  Stability of periodically time-varying systems: Periodic Lyapunov functions , 2012, Autom..

[20]  F. Amato,et al.  On the Region of Asymptotic Stability of Nonlinear Quadratic Systems , 2006, 2006 14th Mediterranean Conference on Control and Automation.

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

[22]  Marco Lovera,et al.  Periodic control of helicopter rotors for attenuation of vibrations in forward flight , 2000, IEEE Trans. Control. Syst. Technol..