Robust control of quadratic systems with norm bounded uncertainties

This paper deals with the problem of the stabilization of uncertain quadratic systems via state feedback. The main contribution of the paper is a control design methodology which enables to find a robust controller guaranteeing for the closed-loop system: i) the local asymptotic stability of the zero equilibrium point; ii) the inclusion of a given polytopic region into the domain of attraction of the zero equilibrium point. This design procedure involves the solution of a Linear Matrix Inequalities (LMIs) feasibility problem, which can be efficiently solved via available optimization algorithms. A numerical example shows the effectiveness of the proposed methodology.

[1]  Vijay Vittal,et al.  Application of the normal form of vector fields to predict interarea separation in power systems , 1997 .

[2]  B. Barmish.  Stabilization of uncertain systems via linear control , 1983 .

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

[4]  A. J. Lotka,et al.  Elements of Physical Biology. , 1925, Nature.

[5]  I. Petersen.  A stabilization algorithm for a class of uncertain linear systems , 1987 .

[6]  F. Amato,et al.  State constrained control of impulsive quadratic systems in integrated pest management , 2012 .

[7]  A. Trofino.  Robust stability and domain of attraction of uncertain nonlinear systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[8]  A. J. Lotka.  Elements of Physical Biology. , 1925, Nature.

[9]  Wilson J. Rugh,et al.  Research on gain scheduling , 2000, Autom..

[10]  Francesco Amato,et al.  Robust Control of Linear Systems Subject to Uncertain Time-Varying Parameters , 2006 .

[11]  O. Rössler.  Chaotic Behavior in Simple Reaction Systems , 1976 .

[12]  E. Feron,et al.  Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions , 1996, IEEE Trans. Autom. Control..

[13]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[14]  Feng Lin,et al.  An optimal control approach to robust control of robot manipulators , 1998, IEEE Trans. Robotics Autom..

[15]  P. Gahinet,et al.  Affine parameter-dependent Lyapunov functions and real parametric uncertainty , 1996, IEEE Trans. Autom. Control..

[16]  Gérard Scorletti,et al.  Control of rational systems using linear-fractional representations and linear matrix inequalities , 1996, Autom..

[17]  Francesco Amato,et al.  State feedback control of nonlinear quadratic systems , 2007, 2007 46th IEEE Conference on Decision and Control.

[18]  A. Tits,et al.  Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics , 1991 .

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

[20]  Francesco Amato,et al.  Output feedback control of nonlinear quadratic systems , 2007, 49th IEEE Conference on Decision and Control (CDC).