Abstract
AbstractThis chapter aims at extending the differential geometric method to design observers for nonlinear singular dynamical systems. Singular systems widely exist in engineering systems, such as chemical system, biological system, electrical circuit and so on. These systems are governed by mixing differential and algebraic equations, which is the key difference with respect to regular systems [5, 6]. Due to this reason, many well-defined concepts relative to observation problem for regular (non-singular) systems have to be reconsidered for singular ones. For such systems, observability has been analyzed in [3, 10], and different types of observers have been proposed in [4, 9, 11]. In this chapter, we will show how to apply differential geometric method to design observers for such a nonlinear singular system [12]. The basic idea is to regularize the studied singular system into a nonlinear regular system with the injection of the output derivative, then seek a diffeomorphism to transform the regularized system into an observer normal form with output derivative injection, based on which a Luenberger-like observer is designed.
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