Simultaneous semi-global Lp-stabilization and asymptotical stabilization for singular systems subject to input saturation

Abstract The simultaneous semi-global L p -stabilization and asymptotic stabilization in both semi-global and global cases are considered for continuous-time linear singular systems subject to input saturation. Based on the asymptotical property of the parametric generalized algebraic Riccati equations, a low-and-high gain state feedback control law and a scheduling technique are proposed. When applied to the singular system subject to input saturation and external disturbance, the semi-global finite-gain L p -stabilization and semi-global/global asymptotic stabilization are obtained simultaneously. The obtained results reduce to the existing ones for non-singular linear systems when the linear singular system reduces to a non-singular system. Furthermore, our results also improve the semi-global stabilization results for singular systems with saturation in the absence of the external disturbance.

[1]  A. Megretski,et al.  L 2 Bibo Output Feedback Stabilization With Saturated Control , 1996 .

[2]  Zongli Lin.  Global Control of Linear Systems with Saturating Actuators , 1998, Autom..

[3]  Liang Lu,et al.  Analysis and design of singular linear systems under actuator saturation and L2/linfintyA disturbances , 2008, Syst. Control. Lett..

[4]  Ali Saberi,et al.  On simultaneous global external and global internal stabilization of critically unstable linear systems with saturating actuators , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[5]  Guang-Ren Duan,et al.  Global Stabilization of the Double Integrator System With Saturation and Delay in the Input , 2010 .

[6]  Weiyao Lan,et al.  Semiglobal stabilization and output regulation of singular linear systems with input saturation , 2003, IEEE Trans. Autom. Control..

[7]  Andrew R. Teel,et al.  Simultaneous L p -stabilization and internal stabilization of linear systems subject to input saturation—state feedback case , 1995 .

[8]  Guang-Ren Duan,et al.  On Analytical Approximation of the Maximal Invariant Ellipsoids for Linear Systems With Bounded Controls , 2009, IEEE Transactions on Automatic Control.

[9]  James Lam,et al.  An ARE approach to semi-global stabilization of discrete-time descriptor linear systems with input saturation , 2009, Syst. Control. Lett..

[10]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[11]  Zongli Lin,et al.  Set Invariance Conditions for Singular Linear Systems Subject to Actuator Saturation , 2007, IEEE Transactions on Automatic Control.

[12]  Zhong-Ping Jiang,et al.  Saturated Feedback Stabilization of Discrete-Time Descriptor Bilinear Systems , 2007, IEEE Transactions on Automatic Control.

[13]  Shengyuan Xu,et al.  Robust Control and Filtering of Singular Systems , 2006 .

[14]  Guang-Ren Duan,et al.  A Parametric Lyapunov Equation Approach to Low Gain Feedback Design for Discrete-time Systems , 2008 .

[15]  Guang-Ren Duan,et al.  Approximation and Monotonicity of the Maximal Invariant Ellipsoid for Discrete-Time Systems by Bounded Controls , 2010, IEEE Transactions on Automatic Control.

[16]  Andrew R. Teel,et al.  The almost disturbance decoupling problem with internal stability for linear systems subject to input saturation - state feedback case , 1996, Autom..

[17]  João Yoshiyuki Ishihara,et al.  On the Lyapunov theorem for singular systems , 2002, IEEE Trans. Autom. Control..

[18]  Ping Hou,et al.  Simultaneous External and Internal Stabilization for Continuous and Discrete-Time Critically Unstable Linear Systems with Saturating Actuators , 1998, Autom..

[19]  Sophie Tarbouriech,et al.  Focal stability of linear descriptor systems with saturating controls /spl epsiv/neralized Riccati and Lyapunov equations approaches , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[20]  Lv Liang,et al.  Analysis and design of singular linear systems under actuator saturation and L2/L∞ disturbances , 2008, 2008 27th Chinese Control Conference.