The disturbance decoupling problem for continuous piecewise affine systems

In this paper we study the disturbance decoupling problem for continuous piecewise affine systems. We establish a set of necessary conditions and a set of sufficient conditions, both geometric in nature, for such systems to be disturbance decoupled. Furthermore, we investigate mode-independent state feedback controllers for piecewise affine systems and provide sufficient conditions for the solvability of the disturbance decoupling problem by state feedback.

[1]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[2]  M. Kanat Camlibel,et al.  Controllability and Stabilizability of a Class of Continuous Piecewise Affine Dynamical Systems , 2014, SIAM J. Control. Optim..

[3]  Naohisa Otsuka.  Disturbance decoupling with quadratic stability for switched linear systems , 2010, Syst. Control. Lett..

[4]  Nahum Shimkin,et al.  Nonlinear Control Systems , 2008 .

[5]  W. Zhonghua,et al.  Robust adaptive deadzone compensation of DC servo system , 2006 .

[6]  Harry L. Trentelman,et al.  Control theory for linear systems , 2002 .

[7]  J. Pearson.  Linear multivariable control, a geometric approach , 1977 .

[8]  G. Basile,et al.  Controlled and conditioned invariants in linear system theory , 1992 .

[9]  A. Morse,et al.  Decoupling and Pole Assignment in Linear Multivariable Systems: A Geometric Approach , 1970 .

[10]  W. Wonham.  Linear Multivariable Control: A Geometric Approach , 1974 .

[11]  M. Kanat Camlibel,et al.  Disturbance decoupling of switched linear systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[12]  Jinglai Shen,et al.  Robust Non-Zenoness of Piecewise Affine Systems with Applications to Linear Complementarity Systems , 2014, SIAM J. Optim..

[13]  G. Basile,et al.  On the observability of linear, time-invariant systems with unknown inputs , 1969 .

[14]  S. Scholtes.  Introduction to Piecewise Differentiable Equations , 2012 .

[15]  G. Basile,et al.  Controlled and conditioned invariant subspaces in linear system theory , 1969 .