State observers of linear control systems with nonlinear outputs

摘要

Since 1970's there has been an extensive study on the design of observers for nonlinear systems. Most current methods lead to the design of an exponential observer. As a necessary condition for the existence of an exponential observer, the linearized counterpart of the nonlinear system must be detectable. In this paper we consider control systems in the following form: x = A(t)x + Bu(t) y{sub}i = (p{sub}i(x))/(q{sub}i(x)), i = 1,.., m where x ∈ R{sup}n, u ∈ R{sup}p is the input and y{sub}i{sup}ls are the output one can measure. We will try to understand under what conditions one can construct an exponential observer for (1).