Synthesis of a global asymptotic stabilizing feedback law for a system satisfying two different sector conditions

Global asymptotic stabilization for a class of nonlinear systems is addressed. The dynamics of these systems are composed of a linear part to which is added some nonlinearities which satisfy two different sector bound conditions depending wether the state is closed or distant from the origin. The approach described here is based on the uniting of control Lyapunov functions as introduced in [2]. The stabilization problem may be recast as an LMI optimization problem for which powerful semidefinite programming softwares exist. This is illustrated by a numerical example.

[1]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[2]  Guido Herrmann,et al.  Advanced Strategies in Control Systems with Input and Output Constraints , 2006 .

[3]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[4]  Alessandro Astolfi,et al.  Homogeneous Approximation, Recursive Observer Design, and Output Feedback , 2008, SIAM J. Control. Optim..

[5]  V. Lakshmikantham,et al.  Nonlinear Analysis: Theory, Methods and Applications , 1978 .

[6]  Karolos M. Grigoriadis,et al.  A unified algebraic approach to linear control design , 1998 .

[7]  Christophe Prieur.  Uniting Local and Global Controllers with Robustness to Vanishing Noise , 2001, Math. Control. Signals Syst..

[8]  Christophe Prieur,et al.  Uniting Two Control Lyapunov Functions for Affine Systems , 2008, IEEE Transactions on Automatic Control.

[9]  Sophie Tarbouriech,et al.  Stability analysis and stabilization of systems presenting nested saturations , 2006, IEEE Transactions on Automatic Control.

[10]  Isabelle Queinnec,et al.  Control design for a class of nonlinear continuous-time systems , 2008, Autom..

[11]  Sophie Tarbouriech,et al.  Antiwindup design with guaranteed regions of stability: an LMI-based approach , 2005, IEEE Transactions on Automatic Control.

[12]  Petar V. Kokotovic,et al.  Circle and Popov criteria as tools for nonlinear feedback design, , 2003, Autom..

[13]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[14]  Emmanuel Trélat,et al.  Quasi-Optimal Robust Stabilization of Control Systems , 2006, SIAM J. Control. Optim..

[15]  Sophie Tarbouriech,et al.  Advanced strategies in control systems with input and output constraints , 2007 .

[16]  Andrew R. Teel,et al.  Uniting local and global controllers , 1997, 1997 European Control Conference (ECC).

[17]  Luca Zaccarian,et al.  Stability and Performance for Saturated Systems via Quadratic and Nonquadratic Lyapunov Functions , 2006, IEEE Transactions on Automatic Control.

[18]  Ricardo C. L. F. Oliveira,et al.  Robust absolute stability and nonlinear state feedback stabilization based on polynomial Lur'e functions , 2009 .

[19]  Z. Artstein.  Stabilization with relaxed controls , 1983 .

[20]  A.R. Teel,et al.  Uniting a high performance, local controller with a global controller: The output feedback case for linear systems with input saturation , 2008, 2008 American Control Conference.