Generality of functional observer structures

Functional observers estimate a linear function of the state vector directly without having to estimate all the individual states. In the past various observer structures have been employed to design such functional estimates. In this paper we discuss the generality of those various observer structures and prove the conditions under which those observer structures are unified. The paper also highlights and clarifies the need to remove the self-convergent states from the system and also from the functions to be estimated before proceeding with the design of a functional observer or else incorrect conclusions regarding the existence of functional observers can be arrived at.

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

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

[3]  T. Bullock,et al.  Design of minimal order stable observers for linear functions of the state via realization theory , 1975 .

[4]  Tyrone Fernando,et al.  Disturbance Decoupled Observers for Systems With Unknown Inputs , 2008, IEEE Transactions on Automatic Control.

[5]  Chia-Chi Tsui.  What is the minimum function observer order , 1998, 2003 European Control Conference (ECC).

[6]  K. Furuta,et al.  Linear function observer with possibly minimal dimension , 1977 .

[7]  Chia-Chi Tsui.  On the Order Reduction of Linear Functional Observers , 1986, 1985 American Control Conference.

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

[9]  Tyrone Fernando,et al.  Partial-State Observers for Nonlinear Systems , 2006, IEEE Transactions on Automatic Control.

[10]  H. Trinh,et al.  On the Existence and Design of Functional Observers for Linear Systems , 2007, 2007 International Conference on Mechatronics and Automation.

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

[12]  Jaime A. Moreno,et al.  Simultaneous observation of linear systems: a state-space interpretation , 2005, IEEE Transactions on Automatic Control.

[13]  Chia-Chi Tsui.  A new algorithm for the design of multifunctional observers , 1985, IEEE Transactions on Automatic Control.

[14]  Chia-Chi Tsui,et al.  Robust Control System Design , 1996 .

[15]  Chia-Chi Tsui,et al.  Robust Control System Design: Advanced State Space Techniques , 1996 .

[16]  J. Moreno,et al.  Quasi-unknown input observers for linear systems , 2001, Proceedings of the 2001 IEEE International Conference on Control Applications (CCA'01) (Cat. No.01CH37204).

[17]  D. Luenberger.  An introduction to observers , 1971 .

[18]  H. Sirisena.  Minimal-order observers for linear functions of a state vector† , 1979 .

[19]  S. Srinathkumar.  Minimal order observers for linear functions of the state vector , 1978 .