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Observer design for nonlinear discrete-time systems: immersion and dynamic observer error linearization techniques. (English) Zbl 1185.93022
Summary: This paper focuses on the observer design for nonlinear discrete-time systems by means of nonlinear observer canonical form. At first, sufficient and necessary conditions are obtained for a class of autonomous nonlinear discrete-time systems to be immersible into higher dimensional observer canonical form. Then a method called dynamic observer error linearization is developed. By introducing a dynamic auxiliary system, the augmented system is shown to be locally equivalent to the generalized observer form, whose nonlinear terms contain auxiliary states and output of the system. A constructive algorithm is also provided to obtain the state coordinate transformation. These results are an extension of their counterparts of nonlinear continuous-time systems to nonlinear discrete-time systems [J. Levine and R. Marino, Syst. Control Lett. 7, 133–142 (1986; Zbl 0592.93030); P. Jouan, SIAM J. Control Optimization 41, No. 6, 1756–1778 (2003; Zbl 1036.93006); J. Back and J. H. Seo, Int. J. Control 77, No. 8, 723–734 (2004; Zbl 1069.93006); Automatica 42, No. 2, 321–328 (2006; Zbl 1099.93007); G. Besancon and A. Ticlea, An immersion-based observer design for rank-observable nonlinear systems, IEEE Trans. Automat. Control 52, 83–88 (2007); D. Noh, Jo, N. H. and J. H. Seo, IEEE Trans. Automat. Control 49, 1746–1750 (2004); J. Back, K. T. Yu and J. H. Seo, Automatica 42, No. 12, 2195–2200 (2006; Zbl 1104.93017); A. Glumineau, C. H. Moog and F. Plestan, IEEE Trans. Autom. Control 41, No. 4, 598–603 (1996; Zbl 0851.93018); F. Plestan and A. Glumineau, Syst. Control Lett. 31, No. 2, 115–128 (1997; Zbl 0901.93013)].

MSC:
93B07 Observability
93B51 Design techniques (robust design, computer-aided design, etc.)
93C10 Nonlinear systems in control theory
93C55 Discrete-time control/observation systems
93B10 Canonical structure
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