Identification and adaptive control of SISO singular systems

A general adaptive control scheme is presented for an unknown time invariant singular system of the form Ex(t + 1) = Ax(t) + Bu(t); y(t) = Cx(t). Owing to the non-causality of this kind of system, the identification of unknown parameters is re-considered and a new residual signal is constructed and used in the recursive calculations. A general design procedure is obtained that uses the identified parameters and includes two steps: (i) preliminary output feedback gain design in order to make the original system causal; (ii) adaptive control design for the causal system. It has been shown that any adaptive control algorithm can be combined with this scheme to obtain a globally stable closed-loop system. The design procedure is shown to perform well on a simulation of a third-order singular system.