Stabilization of uncertain negative-imaginary systems using a Riccati equation approach

In this paper, a stabilization procedure that forces an uncertain system to be stable and satisfy the negative imaginary property is presented. The controller synthesis procedure is based on the negative imaginary lemma. As a result, the closed-loop system can be guaranteed to be robustly stable against any strict negative imaginary uncertainty, such as in the case of unmodeled spill-over dynamics in a lightly damped flexible structure. A numerical example is presented to illustrate the usefulness of the proposed results.

[1]  Alexander Lanzon,et al.  Feedback Control of Negative-Imaginary Systems , 2010, IEEE Control Systems.

[2]  Ian R. Petersen,et al.  Stability analysis for a class of negative imaginary feedback systems including an integrator , 2011, 2011 8th Asian Control Conference (ASCC).

[3]  Bernhard Maschke,et al.  Dissipative Systems Analysis and Control , 2000 .

[4]  A. Ran,et al.  Existence and comparison theorems for algebraic Riccati equations for continuous- and discrete-time systems , 1988 .

[5]  Ian R. Petersen,et al.  A stability result on the feedback interconnection of negative imaginary systems with poles at the origin , 2012, 2012 2nd Australian Control Conference.

[6]  IAN R. PETERSEN,et al.  STABILIZATION OF CONDITIONAL UNCERTAIN NEGATIVE-IMAGINARY SYSTEMS USING RICCATI EQUATION APPROACH , 2012 .

[7]  Ian R. Petersen,et al.  Stability Robustness of a Feedback Interconnection of Systems With Negative Imaginary Frequency Response , 2008, IEEE Transactions on Automatic Control.

[8]  Y. Yong,et al.  Atomic force microscopy with a 12-electrode piezoelectric tube scanner. , 2010, The Review of scientific instruments.

[9]  Allan Waters.  Active Filter Design , 1991 .

[10]  J. L. Fanson,et al.  Positive position feedback control for large space structures , 1990 .

[11]  Arjan van der Schaft,et al.  Positive feedback interconnection of Hamiltonian systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[12]  S. O. Reza Moheimani,et al.  Experimental implementation of extended multivariable PPF control on an active structure , 2006, IEEE Transactions on Control Systems Technology.

[13]  Chaohong Cai,et al.  Stability Analysis for a String of Coupled Stable Subsystems With Negative Imaginary Frequency Response , 2010, IEEE Transactions on Automatic Control.

[14]  Chun-Hua Guo,et al.  Analysis and modificaton of Newton's method for algebraic Riccati equations , 1998, Math. Comput..

[15]  Ian R. Petersen,et al.  A new stability result for the feedback interconnection of negative imaginary systems with a pole at the origin , 2011, IEEE Conference on Decision and Control and European Control Conference.

[16]  Ian R. Petersen,et al.  Stability analysis of negative imaginary systems with real parametric uncertainty – the single-input single-output case , 2010 .

[17]  Mark R. Opmeer,et al.  Infinite-Dimensional Negative Imaginary Systems , 2011, IEEE Transactions on Automatic Control.