L2 Gain Stability of Switched Output Feedback Controllers for a Class of LTI Systems

Our previous work has been devoted to designing asymptotically stabilizing switching controllers for a class of second order LTI plants. Here, we extend the results of our previous work by proving that, when a plant can be asymptotically stabilized using a particular switching architecture, the overall closed-loop interconnection is also finite L2 gain stable. We shall first prove this result for a simplified problem in which a portion of the switching architecture has full access to the state of the plant and shall then extend to the case where the architecture only has access to the plant output by designing an appropriate observer.

[1]  Thomas A. Henzinger,et al.  Hybrid systems III : verification and control , 1996 .

[2]  J. Imae,et al.  gain analysis for switched systems with continuous-time and discrete-time subsystems , 2005 .

[3]  Y. Kim,et al.  L/sub 2/ gain analysis for switched systems with continuous-time and discrete-time subsystems , 2004, SICE 2004 Annual Conference.

[4]  Jorge M. Gonçalves,et al.  Constructive global analysis of hybrid systems , 2000 .

[5]  Panos J. Antsaklis,et al.  Design of stabilizing control laws for second-order switched systems , 1999 .

[6]  K.R. Santarelli,et al.  Optimal Controller Synthesis for Second Order LTI Plants with Switched Output Feedback , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[7]  Keith R. Santarelli On the synthesis of switched output feedback controllers for linear, time-invariant systems , 2007 .

[8]  David A. Johns,et al.  Analog Integrated Circuit Design , 1996 .

[9]  Munther A. Dahleh,et al.  On the stabilizability of two-dimensional linear systems via switched output feedback , 2005, Proceedings of the 2005, American Control Conference, 2005..

[10]  Panos J. Antsaklis,et al.  Stabilization of second-order LTI switched systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[11]  João Pedro Hespanha,et al.  Root-mean-square gains of switched linear systems , 2003, IEEE Trans. Autom. Control..

[12]  R. Stephenson A and V , 1962, The British journal of ophthalmology.

[13]  Munther A. Dahleh,et al.  Comparison between a switching controller and two LTI controllers for a class of LTI plants , 2009 .

[14]  Elena Litsyn,et al.  Stabilization of Linear Differential Systems via Hybrid Feedback Controls , 2000, SIAM J. Control. Optim..

[15]  Carlo Benassi,et al.  Hybrid stabilization of planar linear systems with one-dimensional outputs , 2002, Syst. Control. Lett..

[16]  Jun Zhao,et al.  On Stability and L2-gain for Switched Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[17]  A. Michel,et al.  Hybrid output feedback stabilization of two-dimensional linear control systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[18]  Zvi Artstein,et al.  Examples of Stabilization with Hybrid Feedback , 1996, Hybrid Systems.

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

[20]  J. Doyle,et al.  Essentials of Robust Control , 1997 .

[21]  Bo Hu,et al.  Disturbance attenuation properties of time-controlled switched systems , 2001, J. Frankl. Inst..

[22]  Daniel Liberzon,et al.  Stabilizing a Linear System With Finite-State Hybrid Output Feedback , 1998 .

[23]  Munther A. Dahleh,et al.  Lectures on Dynamic Systems and Control , 2004 .

[24]  Arcady Ponosov,et al.  Classification of Linear Dynamical Systems in the Plane in Admitting a Stabilizing Hybrid Feedback Control , 2000 .

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

[26]  Robert G. Meyer,et al.  Analysis and Design of Analog Integrated Circuits , 1993 .