New LMI conditions for static output feedback synthesis with multiple performance objectives

The static output feedback synthesis problem is considered with ℋ∞ and generalized ℋ2 performance objectives. New sufficient LMI conditions are derived for guaranteeing the required performance objectives. These conditions also depend on scalar parameters that need to be fixed beforehand. The output feedback gain matrix is computed from the involved matrix variables without the use of system matrices. Hence the conditions can directly be used to solve the multi-objective synthesis problem also for parameter-dependent systems with constant or parameter-dependent gain matrices. The method is illustrated in the adaptive cruise control problem.

[1]  Carsten W. Scherer,et al.  LMI Relaxations in Robust Control , 2006, Eur. J. Control.

[2]  Alexandre Trofino,et al.  Sufficient LMI conditions for output feedback control problems , 1999, IEEE Trans. Autom. Control..

[3]  Friedemann Leibfritz,et al.  An LMI-Based Algorithm for Designing Suboptimal Static H2/Hinfinity Output Feedback Controllers , 2000, SIAM J. Control. Optim..

[4]  Qing-Guo Wang,et al.  An Improved ILMI Method for Static Output Feedback Control With Application to Multivariable PID Control , 2006, IEEE Transactions on Automatic Control.

[5]  F. Lewis,et al.  Necessary and Sufficient Conditions for H-∞ Static Output-Feedback Control , 2006 .

[6]  A. Trofino,et al.  A New Strategy to the Multi-Objective Control of Linear Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[7]  Wook Hyun Kwon,et al.  Sufficient LMI conditions for the H/sub /spl infin// output feedback stabilization of linear discrete-time systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[8]  Dimitri Peaucelle,et al.  Some Conditions for Convexifying Static H∞ Control Problems* , 2011 .

[9]  Ian Postlethwaite,et al.  Static output feedback stabilisation with H∞ performance for a class of plants , 2001, Syst. Control. Lett..

[10]  James Lam,et al.  An augmented system approach to static output‐feedback stabilization with ℋ︁∞ performance for continuous‐time plants , 2009 .

[11]  Pierre Apkarian,et al.  Continuous-time analysis, eigenstructure assignment, and H2 synthesis with enhanced linear matrix inequalities (LMI) characterizations , 2001, IEEE Trans. Autom. Control..

[12]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1997, IEEE Trans. Autom. Control..

[13]  Ricardo C. L. F. Oliveira,et al.  Robust state feedback LMI methods for continuous-time linear systems: Discussions, extensions and numerical comparisons , 2011, 2011 IEEE International Symposium on Computer-Aided Control System Design (CACSD).

[14]  Chaouki T. Abdallah,et al.  Static output feedback: a survey , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[15]  Massimiliano Mattei,et al.  Sufficient conditions for the synthesis ofH? fixed-order controllers , 2000 .

[16]  Jalel Zrida,et al.  Sufficient Dilated LMI Conditions for H∞ Static Output Feedback Robust Stabilization of Linear Continuous-Time Systems , 2012, J. Appl. Math..

[17]  Wook Hyun Kwon,et al.  Sufficient LMI conditions for the H∞ output feedback stabilization of linear discrete-time systems , 2004, CDC.

[18]  W. Yan.  Static Output Feedback Stabilization , 2006, TENCON 2006 - 2006 IEEE Region 10 Conference.

[19]  Alexandre Trofino,et al.  Sufficient LMI conditions for the design of static and reduced order controllers , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[20]  Mohamed Boutayeb,et al.  Static output feedback stabilization with H/sub /spl infin// performance for linear discrete-time systems , 2005, IEEE Transactions on Automatic Control.

[21]  James Lam,et al.  Static Output Feedback Stabilization: An ILMI Approach , 1998, Autom..

[22]  Guang-Hong Yang,et al.  Robust static output feedback control synthesis for linear continuous systems with polytopic uncertainties , 2013, Autom..

[23]  Guang-Hong Yang,et al.  Static Output Feedback Control Synthesis for Linear Systems With Time-Invariant Parametric Uncertainties , 2007, IEEE Transactions on Automatic Control.

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