Synthesizing Asymptotic Observers for Hyperoutput Systems with Uncertainty upon Transfer Matrix Degeneracy

The problem of synthesizing an asymptotic observer for a linear system with measurable outputs and unknown inputs acting on the system through the matrix is considered. A case of hyperoutput systems is examined; such systems have output dimensions larger than that of an unknown input ( ). Ways of constructing observers are well-known for such systems when matrix (the transfer matrix from input to output ) is of full rank. The case is considered. To solve the problem, the concept of relative order is generalized to the case of non-quadratic systems. Using this concept, a sufficient condition for the existence of an observer is formulated, and an algorithm for synthesizing the observer is proposed.