Unobservability Subspaces For Continuous-time Markovian Jump Systems with Application to Fault Diagnosis

Abstract This paper introduces the notion of unobservability subspaces for continuous-time Markovian Jump System (MJS) with irreducible Markov process. First a geometric property related to the unobservable subspace of a Markovian jump system is presented. A new approach for determining the conditions for weak-observability of MJS systems is then developed. The concept of an unobservability subspace is presented and an algorithm for obtaining it is described. The necessary and sufficient conditions for solvability of the fundamental problem of residual generation (FPRG) for MJS systems are derived by utilizing our introduced unobservability subspaces.

[1]  Giovanni Marro,et al.  On the robust controlled invariant , 1987 .

[2]  A. Willsky,et al.  Failure detection and identification , 1989 .

[3]  A. Hassibi,et al.  Control with random communication delays via a discrete-time jump system approach , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[4]  James Lam,et al.  Robust H∞ control of uncertain Markovian jump systems with time-delay , 2000, IEEE Trans. Autom. Control..

[5]  Eduardo F. Costa,et al.  On the observability and detectability of continuous-time Markov jump linear systems , 2001, 2001 European Control Conference (ECC).

[6]  Alberto Isidori,et al.  A geometric approach to nonlinear fault detection and isolation , 2000, IEEE Trans. Autom. Control..

[7]  Hassan Hammouri,et al.  A geometric approach to fault detection and isolation for bilinear systems , 2001, IEEE Trans. Autom. Control..

[8]  Richard M. Murray,et al.  On the control of jump linear Markov systems with Markov state estimation , 2003, Proceedings of the 2003 American Control Conference, 2003..

[9]  P.M. Frank,et al.  Fault detection of networked control systems with missing measurements , 2004, 2004 5th Asian Control Conference (IEEE Cat. No.04EX904).

[10]  Gary J. Balas,et al.  Detection filter design for LPV systems - a geometric approach , 2004, Autom..

[11]  H. Ye,et al.  Fault detection for Markovian jump systems , 2005 .

[12]  Richard M. Murray,et al.  State estimation over packet dropping networks using multiple description coding , 2006, Autom..

[13]  James Lam,et al.  Fixed-order robust H/sub /spl infin// filter design for Markovian jump systems with uncertain switching probabilities , 2006, IEEE Transactions on Signal Processing.

[14]  Ligang Wu,et al.  An LMI approach to fault detection and isolation filter design for Markovian jump system with mode-dependent time-delays , 2006, 2006 American Control Conference.

[15]  Zehui Mao,et al.  H/sub /spl infin// fault detection filter design for networked control systems modelled by discrete Markovian jump systems , 2007 .

[16]  K. Khorasani,et al.  A geometric approach to robust Fault Detection and Isolation of discrete-time Markovian jump systems , 2008, 2008 American Control Conference.

[17]  Khashayar Khorasani,et al.  Robust fault detection and isolation of time-delay systems using a geometric approach , 2009, Autom..