Adaptive control of linear singular time-invariant single-input single-output systems with external point delay

This paper is devoted to the robust adaptive control of solvable single-input single-output impulse-free linear time-invariant singular dynamic systems of known orders and unknown parameterizations subject to single external point delays. The control law is of pole-placement type and based on input/output measurements and parametrical estimation only. The parametrical estimation algorithm incorporates adaptation dead zones to prevent against potential instability caused by disturbances and unmodeled dynamics. The Weierstrass canonical form is investigated in detail concerning the properties of controllability and observability via testable conditions of the given arbitrary state-space realization of the same order. Robust closed-loop stability is proved under similar conditions to those used for (nonsingular) standard systems.