Far East Journal of Dynamical Systems
Volume 13, Issue 1, Pages 43 - 60
(May 2010)
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NONLINEAR OBSERVER DESIGN FOR A GENERAL CLASS OF DISCRETE-TIME NONLINEAR SYSTEMS WITH REAL PARAMETRIC UNCERTAINTY AROUND EQUILIBRIA
V. Sundarapandian
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Abstract:
This paper is a geometric study of the local observer design for a general class of discrete-time nonlinear systems with real parametric uncertainty around equilibria. In this paper, we derive several results for the local asymptotic and exponential observer design problems for a general class of discrete-time nonlinear systems with real parametric uncertainty. In this paper, we first show that equilibrium-state detectability is a necessary condition for the existence of local asymptotic observers for any nonlinear system and using this result, we show that for the classical case, when the state equilibrium does not change with the real parametric uncertainty, and when the plant output is purely a function of the state, there is no local asymptotic observer for the plant. Next, we show that in sharp contrast to this case, for the general case of problems where we allow the state equilibrium to change with the real parametric uncertainty, there typically exist local exponential observers even when the plant output is purely a function of the state. We also present a characterization and construction procedure for local exponential observers for a general class of discrete-time nonlinear systems with real parametric uncertainty under some stability assumptions. We also show that for the general class of nonlinear systems considered, under some stability assumptions, the existence of local exponential observers in the presence of inputs implies, and is implied by the existence of local exponential observers in the absence of inputs. |
| Keywords and phrases: nonlinear observers, exponential observers, discrete-time systems, real parametric uncertainty. |
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