Robust decentralized stabilization of Markovian jump large-scale systems: A neighboring mode dependent control approach

Abstract This paper is concerned with the decentralized stabilization problem for a class of uncertain large-scale systems with Markovian jump parameters. The controllers use local subsystem states and neighboring mode information to generate local control inputs. A sufficient condition involving rank constrained linear matrix inequalities is proposed for the design of such controllers. A numerical example is given to illustrate the developed theory.

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

[2]  James Lam,et al.  Stabilization of Markovian Systems via Probability Rate Synthesis and Output Feedback , 2010, IEEE Transactions on Automatic Control.

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

[4]  I. Petersen,et al.  Robust Control Design Using H-? Methods , 2012 .

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

[6]  Yun Zou,et al.  Robust exponential stabilization for Markovian jump systems with mode-dependent input delay , 2007, Autom..

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

[8]  V. Ugrinovskii *,et al.  Decentralized control of power systems via robust control of uncertain Markov jump parameter systems , 2005 .

[9]  C.E. de Souza,et al.  Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems , 2006, IEEE Transactions on Automatic Control.

[10]  Li Li,et al.  On Necessary and Sufficient Conditions for ${H}_{\infty }$ Output Feedback Control of Markov Jump Linear Systems , 2007, IEEE Transactions on Automatic Control.

[11]  Huijun Gao,et al.  New results on stabilization of Markovian jump systems with time delay , 2009, Autom..

[12]  Andrew Brennan,et al.  Necessary and Sufficient Conditions , 2018, Logic in Wonderland.

[13]  Guang-Hong Yang,et al.  Robust H2 control of continuous-time Markov jump linear systems , 2008, Autom..

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

[15]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

[16]  Peng Shi,et al.  Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters , 1999, IEEE Trans. Autom. Control..

[17]  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).

[18]  Javad Mohammadpour,et al.  Efficient modeling and control of large-scale systems , 2010 .

[19]  Shengyuan Xu,et al.  Robust H∞ control for uncertain stochastic systems with state delay , 2002, IEEE Trans. Autom. Control..

[20]  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.