Observer design using a generalized time-scaled block triangular observer form

This paper presents an observer design for uncontrolled nonlinear multi-output continuous-time systems based on a Time-scaled Block Triangular Observer Form (TBTOF). The TBTOF generalizes an established Block Triangular Observer Form (BTOF) by including generalized Time Scaling Functions (TSFs) which have both state and output dependence. Introducing these stability preserving TSFs broadens the class of systems which admits a BTOF-based observer design. Necessary conditions for the TSFs are provided. When a TBTOF exists, an observer can be constructed subsystem-at-a-time. Sufficient conditions are given to prove estimate error stability. A physical example illustrates the TBTOF construction and observer design.