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Observer design using a generalized time-scaled block triangular observer form. (English) Zbl 1159.93327
Summary: This paper presents an observer design for uncontrolled nonlinear multi-output continuous-time systems based on a Time-scaled Block Triangular Observer Form (TBTOF). The TBTOF generalizes an established Block Triangular Observer Form (BTOF) by including generalized Time Scaling Functions (TSFs) which have both state and output dependence. Introducing these stability preserving TSFs broadens the class of systems which admits a BTOF-based observer design. Necessary conditions for the TSFs are provided. When a TBTOF exists, an observer can be constructed subsystem-at-a-time. Sufficient conditions are given to prove estimate error stability. A physical example illustrates the TBTOF construction and observer design.

MSC:
93B51 Design techniques (robust design, computer-aided design, etc.)
93B07 Observability
93C15 Control/observation systems governed by ordinary differential equations
93C35 Multivariable systems, multidimensional control systems
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[1] Krener, A.J.; Isidori, A., Linearization by output injection and nonlinear observers, Systems and control letters, 3, 1, 47-52, (1983) · Zbl 0524.93030
[2] Bestle, D.; Zeitz, M., Canonical form observer design for non-linear time-variable systems, International journal of control, 38, 2, 419-431, (1983) · Zbl 0521.93012
[3] Krener, A.J.; Respondek, W., Nonlinear observers with linearizable error dynamics, SIAM journal on control and optimization, 23, 2, 197-216, (1985) · Zbl 0569.93035
[4] Xia, X.-H.; Gao, W.-B., Non-linear observer design by observer canonical form, International journal of control, 47, 4, 1081-1100, (1988) · Zbl 0643.93011
[5] Hou, M.; Pugh, A., Observer with linear error dynamics for nonlinear multi-input systems, Systems and control letters, 37, 1, 1-9, (1999) · Zbl 0917.93010
[6] Lynch, A.F.; Bortoff, S.A., Nonlinear observers with approximately linear error dynamics: the multivariable case, IEEE transactions on automatic control, AC-46, 6, 927-932, (2001) · Zbl 1037.93014
[7] Marino, R.; Tomei, P., Adaptive observers with arbitrary exponential rate of convergence for nonlinear systems, IEEE transactions on automatic control, AC-40, 7, 1300-1304, (1995) · Zbl 0832.93009
[8] Levine, J.; Marino, R., Nonlinear system immersion. observers and finite-dimensional filters, Systems and control letters, 7, 2, 133-142, (1986) · Zbl 0592.93030
[9] Back, J.; Seo, J.H., Immersion of nonlinear systems into linear systems up to output injection: characteristic equation approach, International journal of control, 77, 8, 723-734, (2004) · Zbl 1069.93006
[10] Back, J.; Seo, J.H., An algorithm for system immersion into nonlinear observer form: SISO case, Automatica, 42, 2, 321-328, (2006) · Zbl 1099.93007
[11] Noh, D.; Seo, N.Jo., Nonlinear observer design by dynamic observer error linearization, IEEE transactions on automatic control, AC-49, 10, 1746-1753, (2004) · Zbl 1365.93060
[12] Rudolph, J.; Zeitz, M., Block triangular nonlinear observer normal form, Systems and control letters, 23, 1, 1-8, (1994) · Zbl 0818.93006
[13] Wang, Y.; Lynch, A., A block triangular form for nonlinear observer design, IEEE transactions on automatic control, AC-51, 11, 1803-1808, (2006) · Zbl 1366.93084
[14] Wang, Y.; Lynch, A., A block triangular observer form for non-linear observer design, International journal of control, 81, 2, 177-188, (2008) · Zbl 1152.93319
[15] Sampei, M.; Furuta, K., On time scaling for nonlinear systems: applications to linearization, IEEE transactions on automatic control, AC-31, 5, 459-462, (1986) · Zbl 0611.93037
[16] W. Respondek, Orbital feedback linearization of single-input nonlinear control systems, in: Proceedings of the IFAC Nonlinear Control Systems Design Symposium NOLCOS’98, Enschede, Holland, July 1998, pp. 499-504
[17] Guay, M., An algorithm for orbital feedback linearization of single-input control affine systems, Systems and control letters, 38, 4, 271-281, (1999) · Zbl 0985.93009
[18] Respondek, W.; Pogromsky, A.; Nijmeijer, H., Time scaling for observer design with linearizable error dynamics, Automatica, 40, 2, 277-285, (2004) · Zbl 1055.93010
[19] Guay, M., Observer linearization by output-dependent time-scaling transformation, IEEE transactions on automatic control, AC-47, 10, 1730-1735, (2002) · Zbl 1364.93087
[20] Y. Wang, A.F. Lynch, Observer design using a time scaled block triangular observer form, in: Proceedings of the 2006 American Control Conference, Minneapolis, MN, June 2006, pp. 799-804
[21] Y. Wang, A.F. Lynch, Time scaling of a multi-output observer form, in: Proceedings of the 2008 American Control Conference, Seattle, WA, June 2008, pp. 5242-5247
[22] Nijmeijer, H., Observability of a class of nonlinear systems: A geometric approach, Ricerche di automatica, 12, 1, 1107-1130, (1981) · Zbl 0523.93018
[23] Gauthier, J.P.; Hammouri, H.; Othman, S., A simple observer for nonlinear systems — applications to bioreactors, IEEE transactions on automatic control, AC-37, 6, 875-880, (1992) · Zbl 0775.93020
[24] Schaffner, J.; Zeitz, M., Variants of nonlinear normal form observer design, (), 161-180 · Zbl 0949.93010
[25] Chen, X.; Kano, H., A new state observer for perspective systems, IEEE transactions on automatic control, 47, 4, 658-663, (2002) · Zbl 1364.93082
[26] O. Dahl, Y. Wang, A.F. Lynch, A. Heyden, Observer forms for perspective systems, in: Proceedings of the 2008 IFAC World Congress, Seoul, Korea, July 2008, pp. 8618-8623
[27] Shim, H.; Son, Y.I.; Seo, J.H., Semi-global observer for multi-output nonlinear systems, Systems and control letters, 42, 3, 233-244, (2001) · Zbl 0985.93006
[28] Khalil, H.K., Nonlinear systems, (2002), Prentice-Hall Englewood Cliffs, NJ · Zbl 0626.34052
[29] Schaffner, J.; Zeitz, M., Decentral nonlinear observer design using a block-triangular form, International journal of systems science, 30, 10, 1131-1142, (1999) · Zbl 1090.93527
[30] Hauser, J.; Sastry, S.; Kokotović, P., Nonlinear control via approximate input-output linearization: the ball and beam example, IEEE transactions on automatic control, AC-37, 3, 392-398, (1992)
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