Minimal single linear functional observers for discrete-time linear systems

In this paper, the direct approach which was introduced for the first time by [Rotella and Zambettakis, 2011] in designing minimal functional state observers is extended to deal with discrete-time systems. One of the benefits of this approach is that it does not require solving the Sylvester matrix equation that appears in other observer design procedures. Both stable observers and arbitrary fixed poles observers problems are considered for minimality. A numerical example and simulation results explain the effectiveness and the benefits of the proposed algorithm.

[1]  Mohamed Darouach.  Existence and design of functional observers for linear systems , 2000, IEEE Trans. Autom. Control..

[2]  Frédéric Rotella,et al.  A direct design procedure for linear state functional observers , 2016, Autom..

[3]  Frédéric Rotella,et al.  Minimal single linear functional observers for linear systems , 2011, Autom..

[4]  D. Luenberger.  Observers for multivariable systems , 1966 .

[5]  Tyrone Fernando,et al.  Functional Observability and the Design of Minimum Order Linear Functional Observers , 2010, IEEE Transactions on Automatic Control.

[6]  G. R. DUAN,et al.  Solution to matrix equation AV + BW = EVF and eigenstructure assignment for descriptor systems , 1992, Autom..

[7]  Kit Po Wong,et al.  Quasi-Decentralized Functional Observers for the LFC of Interconnected Power Systems , 2013, IEEE Transactions on Power Systems.

[8]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[9]  D. Williamson,et al.  Design of low-order observers for linear feedback control laws , 1972 .

[10]  Tyrone Fernando,et al.  Existence Conditions for Functional Observability From an Eigenspace Perspective , 2011, IEEE Transactions on Automatic Control.

[11]  Frédéric Rotella,et al.  On Functional Observers for Linear Time-Varying Systems , 2013, IEEE Transactions on Automatic Control.

[12]  Frédéric Rotella,et al.  A Note on Functional Observability , 2016, IEEE Transactions on Automatic Control.

[13]  Hieu Trinh,et al.  Reduced-order linear functional observer for linear systems , 1999 .

[14]  Saeid Nahavandi,et al.  Minimal multi-functional observers for linear systems using a direct approach , 2015, 2015 IEEE Conference on Control Applications (CCA).

[15]  Saeid Nahavandi,et al.  Design of scalar functional observers of order less than (ν − 1) , 2006 .