LMI-Based Sliding Surface Design for Integral Sliding Mode Control of Mismatched Uncertain Systems

We propose a linear matrix inequality (LMI)-based sliding surface design method for integral sliding-mode control of mismatched uncertain systems. The uncertain system under consideration may have mismatched norm bounded uncertainties in the state matrix as well as the input matrix. We give a sufficient condition for the existence of a sliding surface guaranteeing asymptotic stability of the full order sliding mode dynamics. We also give an LMI characterization of the sliding surface, together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time. Additionally, we give an LMI condition of sliding surfaces guaranteeing the alpha-stability constraint. Finally, we give a simulation result to show the effectiveness of our method

[1]  Christopher Edwards,et al.  Linear matrix inequality methods for designing sliding mode output feedback controllers , 2003 .

[2]  Han Ho Choi,et al.  An LMI-based switching surface design method for a class of mismatched uncertain systems , 2003, IEEE Trans. Autom. Control..

[3]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[4]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[5]  V. Utkin,et al.  Sliding mode control design based on Ackermann's formula , 1998, IEEE Trans. Autom. Control..

[6]  Alexander Weinmann.  Uncertain Models and Robust Control , 2002 .

[7]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[8]  Han Ho Choi,et al.  A new method for variable structure control system design: A linear matrix inequality approach , 1997, Autom..

[9]  Ricardo H. C. Takahashi,et al.  H2 guaranteed cost-switching surface design for sliding modes with nonmatching disturbances , 1999, IEEE Trans. Autom. Control..

[10]  John Y. Hung,et al.  Variable structure control: a survey , 1993, IEEE Trans. Ind. Electron..

[11]  Han Ho Choi.  On the existence of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties , 1999, Autom..

[12]  Jian-Xin Xu,et al.  Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems , 2004, IEEE Transactions on Automatic Control.

[13]  R. Decarlo,et al.  Variable structure control of nonlinear multivariable systems: a tutorial , 1988, Proc. IEEE.

[14]  Kyung-Soo Kim,et al.  Designing robust sliding hyperplanes for parametric uncertain systems: a Riccati approach , 2000, Autom..

[15]  Yuanqing Xia,et al.  Robust sliding-mode control for uncertain time-delay systems: an LMI approach , 2003, IEEE Trans. Autom. Control..

[16]  V. Utkin,et al.  Integral sliding mode in systems operating under uncertainty conditions , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[17]  Han Ho Choi,et al.  Variable structure output feedback control design for a class of uncertain dynamic systems , 2002, Autom..

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