Observer Design for MIMO Non-Uniformly Observable Systems

The design of high gain observers is usually based on normal forms of observability. If the system is observable for every input (uniform observability), the gain of the observer does not required a solution to differential equation. For multiple input multiple output (MIMO) non-uniformly observable systems, we give here a sufficient condition that the input must satisfy in order to design an observer. Unlike uniformly observable systems, the observer gain of non-uniformly observable systems is derived from a Lyapunov differential equation.