Implementation of switching law constrained for controlling of switched linear systems
A special class of switched linear systems with switching law constrained to logical state-input can be employed to model a wide range of different systems. The present paper presents a new stability analysis and controller design method for this class of hybrid systems. Proposed methods is based on the quadratic Lyapunov function. Stability analysis and design of these systems have resulted in solving a convex optimization problem of Linear Matrix Inequality type. The results of simulation on dc-dc buck converter confirm the effectiveness of proposed method.
Bemporad, A., Borrelli, F., Morari, M. (2002). “Model predictive control based on linear programming—The explicit solution,” IEEE Trans. Autom. Control, Vol. 47, pp. 1974–1985.
Bemporad, A., Morari, M. (1999). “Control of systems integrating logic, dynamics, and constraints,” Automatica, Vol. 35, No. 3, pp. 407– 427.
Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, Philadelphia, The SIAM press.
Ge, S.S., Sun, Z. (2008). “Switched Controllability via Bumpless Transfer Input and Constrained Switching,” IEEE Trans. On Automatic Control, Vol. 53, No. 7.
Greco, L. (2005). “Stability and Stabilization Issues in Switched Systems,” PHD thesis, Bioingegneria, Robotica e Sistemi di Automazione Industriale - Ciclo XVII.
Hejri, M., Mokhtari, H. (2009). “Global hybrid modeling and control of a buck converter: A novel concept,” International Journal of Circuit Theory and Applications, Vol 37, pp 968–986.
Hejri, M., Mokhtari, H. (2010). “Hybrid predictive control of a DC–DC boost converter in both continuous and discontinuous current modes of operation,” Optimal Control Applications and Methods.
Johansson, M. (2002). Piecewise Linear Control Systems-A Computational Approach, New York: Springer-Verla, Vol, 284.
Lin, H., Panos, J. (2009). Antsaklis, “Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results,” IEEE Trans. Automatic Control, Vol. 54, No. 2.
Pettersson, S., Lennartson, B. (2001). “Stabilization of hybrid systems using a min projection strategy,” in Proc. Amer. Control Conf, pp. 223– 228.
Pettersson, S., Lennartson, B. (2002). “Hybrid system stability and robustness verification using linear matrix inequalities,” Inter. J. Control, Vol. 75,N. 16-17, pp. 1335–1355.
Rantzer, A., Johansson, M. (2000). “Piecewise linear quadratic optimal control,” IEEE Trans. Automat Control, Vol. 45, No. 4, pp. 629–637.
Rodrigues, L. (2002). "Dynamic Output Feedback Controller Synthesis for Piecewise Affine Systems," PhD Thesis, Stanford university.
Rodrigues, L., How, J.P. (2003). “Observer-based control of piecewise-affine systems,” Internat. J. Control, Vol. 76, pp. 459–477.
Sen, M., A. Ibeas, A.(2008) “Stability Results for Switched Linear Systems with Constant Discrete Delays,” Mathematical Problems in Engineering, vol. 2008.
Shorten, R., Wirth, F., Mason, O., Wulff, K., King, K. (2007). “Stability Criteria for Switched and Hybrid Systems,” SIAM REVIEW, Vol. 49, No. 4, pp. 545–592.
Sulistyaningsih, D., & Aziz, A. (2018). Development of Learning Design for Mathematics Manipulatives Learning based on E-learning and Character Building. International Electronic Journal of Mathematics Education, 14(1), 197-205.
Sun, Z., Shuzhi S.G. (2004). Switched Linear Systems: Control and Design, Springer-Verlag Publication.
Uhlig, F. (1979). “A recurring theorem about pairs of quadratic forms and extensions: A survey,” Linear Algebra and Applications, Vol. 25, pp 219-237.
Yakubovich, V.A. (1977). “The S procedure in non-linear control theory,” Vestnik Leningrad Univ. Math, Vol. 4, pp 73-93.