Algorithmic Issues in the Synthesis of Dissipative Systems

In this paper we discuss algorithmic issues that arise in the problem of synthesis of dissipative systems. We deal with linear differential systems that can be controlled only through a restricted set of variables called the control variables. The main feature of this paper is that we assume the system dynamics to be specified in the most general form: a latent variable representation. Starting from such a representation, we provide concrete algorithms that finally fetch a controller to implement the desired behavior. Many other peripheral algorithmic issues that crop up are also studied.

[1]  S. Liberty,et al.  Linear Systems , 2010, Scientific Parallel Computing.

[2]  P. Khargonekar,et al.  State-space solutions to standard H2 and H∞ control problems , 1988, 1988 American Control Conference.

[3]  Michael Green,et al.  A J-Spectral Factorization Approach to H∞ Control , 1990 .

[4]  Michael Green,et al.  H8 controller synthesis by J-lossless coprime factorization , 1992 .

[5]  Harry L. Trentelman,et al.  On quadratic differential forms , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[6]  Jan C. Willems,et al.  Introduction to mathematical systems theory: a behavioral approach, Texts in Applied Mathematics 26 , 1999 .

[7]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[8]  J. Willems,et al.  Every storage function is a state function , 1997 .

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

[10]  Harry L. Trentelman,et al.  New Algorithms for Polynomial J-Spectral Factorization , 1999, Math. Control. Signals Syst..

[11]  J. Willems,et al.  Synthesis of dissipative systems using quadratic differential forms: part II , 2002, IEEE Trans. Autom. Control..

[12]  J. Willems,et al.  Synthesis of dissipative systems using quadratic differential forms: Part I , 2002, IEEE Trans. Autom. Control..

[13]  Arjan van der Schaft,et al.  Achievable behavior of general systems , 2003, Syst. Control. Lett..

[14]  Harry L. Trentelman,et al.  The strict dissipativity synthesis problem and the rank of the coupling QDF , 2004, Syst. Control. Lett..