ABSTRACT
This chapter describes a specific class of dynamical systems—so-called observers—used primarily to estimate the unmeasurable state vector in a state-space system based only on information about the inputs and outputs. It focuses on linear systems and describes some straightforward extensions to nonlinear systems. These ideas, since their inception in the 1960s, have found a wide range of applications: as part of state-feedback control schemes, filtering of noisy data, as a basis for fault detection schemes for dynamical systems, as part of disturbance estimation schemes for improved control, and as a technology for cryptography. In engineering systems, other unmeasurable and unmodeled factors impact on the plant dynamics, and if unaccounted for, will corrupt the state estimation. The work of A. Isidori and coworkers to convert a general class of nonlinear systems to linear ones, via nonlinear coordinate transformation, has also been employed to design observers for a reasonably general class of nonlinear systems.
