ABSTRACT
This chapter provides sufficient conditions for an asymptotic observer and these conditions are conservative. Satisfaction of the conditions does not of itself constitute a constructive procedure for determining a stabilizing gain matrix K. A system–observer structure forms a closed loop system and would preserve the closed loop system poles that would have been obtained if the linear perfect state feedback control had been utilized. The chapter discusses nonlinear systems based on analysis by the Lyapunov method and explains related implementation aspects. The problem of estimating the state of a dynamic system from its input/output data/signals is commonly known as ‘observing the state’, and hence the name observer has become synonymous with filtering. Accordingly, any other system driven by the output of the given system can serve as an observer for that system. In certain control system applications, one is interested in having information about system state variables at any time instant.
