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On the Existence of a Block Triangular Form

This paper extends previously derived existence conditions for a block triangular form (BTF). The BTF can be applied to a broad class of multi-output nonlinear systems. The BTF decomposes a multi-output nonlinear system into subsystems where the dynamics of the ith subsystem depend on the state of the ith subsystem itself, the states of the upper jth subsystem, j < i, and the system output which is a function of all subsystem states. Necessary and sufficient conditions are given to ensure the system admits BTF coordinates. Systems transformable into BTF coordinates allow for a decentralized observer design performed subsystem-at-a-time effectively treating upper subsystems states as measurements. An example illustrates the BTF construction for a system which violates conditions required in previous work on BTF.