Switched Affine Systems Using Sampled-Data Controllers: Robust and Guaranteed Stabilization

The problem of robust and guaranteed stabilization is addressed for switched affine systems using sampled state feedback controllers. Based on the existence of a control Lyapunov function for a relaxed system, we propose three sampled-data controls. Global attracting sets, computed by solving a sequence of optimization problems, guarantee practical and global asymptotic stabilization for the whole system trajectories. In addition, robust margins with respect to parameters uncertainties and non uniform sampling are provided using input-to-state stability. Finally, a buck-boost converter is considered to illustrate the effectiveness of the proposed approaches.

[1]  Stefan Almér,et al.  Stability Analysis of a Class of PWM Systems , 2007, IEEE Transactions on Automatic Control.

[2]  J. Lasserre.  Moments, Positive Polynomials And Their Applications , 2009 .

[3]  Grace S. Deaecto,et al.  Switched affine systems control design with application to DCߝDC converters , 2010 .

[4]  Jamal Daafouz,et al.  Stabilization of Arbitrary Switched Linear Systems With Unknown Time-Varying Delays , 2006, IEEE Transactions on Automatic Control.

[5]  A.G. Beccuti,et al.  Optimal Control of the Buck dc-dc Converter Operating in Both the Continuous and Discontinuous Conduction Regimes , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[6]  Pierre Riedinger,et al.  Practical optimal state feedback control law for continuous-time switched affine systems with cyclic steady state , 2009, Int. J. Control.

[7]  Eduardo F. Camacho,et al.  Min-max Model Predictive Control of Nonlinear Systems: A Unifying Overview on Stability , 2009, Eur. J. Control.

[8]  J. M. Noworolski,et al.  Generalized averaging method for power conversion circuits , 1990, 21st Annual IEEE Conference on Power Electronics Specialists.

[9]  Basil Kouvaritakis,et al.  Receding Horizon Control of Switching Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[10]  Hebertt Sira-Ramírez,et al.  Sliding mode control of DC‐to‐DC power converters using integral reconstructors , 2002 .

[11]  Didier Henrion,et al.  GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi , 2003, TOMS.

[12]  B. T. Baumrucker,et al.  MPEC strategies for optimization of a class of hybrid dynamic systems , 2009 .

[13]  Eduardo Sontag,et al.  New characterizations of input-to-state stability , 1996, IEEE Trans. Autom. Control..

[14]  Eduardo D. Sontag,et al.  An infinite-time relaxation theorem for differential inclusions , 2001 .

[15]  Shouchuan Hu.  Differential equations with discontinuous right-hand sides☆ , 1991 .