Robust Constrained Regulator Problem for Linear Uncertain Systems

The robust regulator problem for linear uncertain systems with constrained control is considered. Necessary and su.cient conditions of positive invariance of polyhedral domains with respect to motion of uncertain systems are given. Further, it is shown that in contrast to the case of perfectly known systems, positive invariance with respect to uncertain systems and stability of n - m assigned eigenvalues from the open loop system do not imply asymptotic stability. Furthermore, conditions ensuring this asymptotic stability are derived. This enables us to construct robust constrained regulators, i.e., control laws satisfying control constraints and achieving asymptotic stability in presence of parametric uncertainties.

[1]  F. Tadeo,et al.  Robust constrained regulator problem for linear uncertain continuous-time systems: application to a pH-process , 2002, Proceedings of the International Conference on Control Applications.

[2]  Eugênio B. Castelan,et al.  Eigenstructure assignment for state constrained linear continuous time systems , 1992, Autom..

[3]  E. Gravalou,et al.  Robust linear controller under state and control constraints , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[4]  Giovanni Muscato,et al.  Bibliography on robust control , 1993, Autom..

[5]  C. Burgat,et al.  Existence of non-symmetrical Lyapunov functions for linear systems , 1989 .

[6]  C. Burgat,et al.  Regulator problem for linear discrete-time systems with non-symmetrical constrained control , 1988 .

[7]  Wei-Bin Gao,et al.  STABILITY OF INTERVAL PARAMETER MATRICES , 1987 .

[8]  A. Benzaouia,et al.  Regulator problem for uncertain linear discrete-time systems with constrained control , 1994 .

[9]  Franco Blanchini.  Feedback control for linear time-invariant systems with state and control bounds in the presence of disturbances , 1990 .

[10]  Per-Olof Gutman,et al.  A new design of constrained controllers for linear systems , 1985, IEEE Transactions on Automatic Control.

[11]  Zongli Lin,et al.  Semi-global Exponential Stabilization of Linear Systems Subject to \input Saturation" via Linear Feedbacks , 1993 .

[12]  A. Hmamed,et al.  Regulator problem for linear continuous-time systems with nonsymmetrical constrained control , 1993, IEEE Trans. Autom. Control..

[13]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[14]  Mario Sznaier,et al.  Robust Systems Theory and Applications , 1998 .

[15]  Bor-Sen Chen,et al.  The stability of feedback control with nonlinear saturating actuator: time domain approach , 1988 .

[16]  Andrew Bartlett,et al.  Robust Control: Systems with Uncertain Physical Parameters , 1993 .

[17]  F. Blanchini.  Constrained control for uncertain linear systems , 1991 .

[18]  Per-Olof Gutman.  Stabilizing controllers for bilinear systems , 1981 .

[19]  Basílio E. A. Milani,et al.  Robust linear regulator design for discrete-time systems under polyhedral constraints , 1995, Autom..

[20]  A. Benzaouia,et al.  The resolution of equation XA+XBX=HX and the pole assignment problem , 1994, IEEE Trans. Autom. Control..

[21]  Zongli Lin,et al.  Semi-global exponential stabilization of linear discrete-time systems subject to input saturation via linear feedbacks , 1995 .