Local Mode Dependent Decentralized $H_{\infty}$ Control of Uncertain Markovian Jump Large-scale Systems

This paper considers the problem of robust $H_{\infty}$ control using decentralized state feedback controllers for a class of large-scale systems with Markov jump parameters. A sufficient condition is developed to design controllers using local system states and local system operation modes. The sufficient condition is given in terms of rank constrained linear matrix inequalities. An illustrative numerical example is given to demonstrate the developed theory.

[1]  E. Boukas,et al.  H ∞ control of a class of extended markov jump linear systems , 2009 .

[2]  Michael Athans,et al.  Survey of decentralized control methods for large scale systems , 1978 .

[3]  James Lam,et al.  Robust H 2 control of Markovian jump systems with uncertain switching probabilities , 2009, Int. J. Syst. Sci..

[4]  K. Loparo,et al.  Stochastic stability properties of jump linear systems , 1992 .

[5]  John B. Moore,et al.  A Newton-like method for solving rank constrained linear matrix inequalities , 2004, CDC.

[6]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..

[7]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[8]  Li Li,et al.  Decentralized robust control of uncertain Markov jump parameter systems via output feedback , 2006, 2006 American Control Conference.

[9]  Ian R. Petersen,et al.  A Rank Constrained LMI Algorithm for Decentralized State Feedback Guaranteed Cost Control of Uncertain Systems with Uncertainty Described by Integral Quadratic Constraints , 2007, 2007 American Control Conference.

[10]  Marcelo D. Fragoso,et al.  Infinite Markov Jump Bounded Real Lemma , 2007, 2007 American Control Conference.

[11]  H.R. Pota,et al.  Decentralized control of power systems via robust control of uncertain Markov jump parameter systems , 2005, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[12]  Ian R. Petersen,et al.  Decentralized state feedback guaranteed cost control of uncertain systems with uncertainty described by integral quadratic constraints , 2006, 2006 American Control Conference.

[13]  Ian R. Petersen,et al.  Decentralized Output Feedback Guaranteed Cost Control of Uncertain Markovian Jump Large-Scale Systems: Local Mode Dependent Control Approach , 2010 .

[14]  E. Boukas,et al.  Stability and robust stabilisation for uncertain discrete stochastic hybrid singular systems with time delay , 2009 .

[15]  Li Li,et al.  On necessary and sufficient conditions for H∞ output feedback control of Markov jump linear systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[16]  James Lam,et al.  H∞ model reduction of Markovian jump linear systems , 2003, Syst. Control. Lett..

[17]  John B. Moore,et al.  A Newton-like method for solving rank constrained linear matrix inequalities , 2006, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[18]  R. Skelton,et al.  The XY-centring algorithm for the dual LMI problem: a new approach to fixed-order control design , 1995 .

[19]  I. Petersen,et al.  Decentralized state-feedback stabilization and robust control of uncertain large-scale systems with integrally constrained interconnections , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[20]  José Claudio Geromel,et al.  Output feedback control of Markov jump linear systems in continuous-time , 2000, IEEE Trans. Autom. Control..

[21]  Ian R. Petersen,et al.  Local Mode Dependent Decentralized Stabilization of Uncertain Markovian Jump Large-Scale Systems , 2009, IEEE Transactions on Automatic Control.