  This paper introduces an innovative singularity-free output feedback model
reference adaptive control (MRAC) method applicable to a wide range of
continuous-time linear time-invariant (LTI) systems with general relative
degrees. Unlike existing solutions such as Nussbaum and multiple-model-based
methods, which manage unknown high-frequency gains through persistent switching
and repeated parameter estimation, the proposed method circumvents these issues
without prior knowledge of the high-frequency gain or additional design
conditions. The key innovation of this method lies in transforming the
estimation error equation into a linear regression form via a modified MRAC law
with a piecewise constant tuning gain developed in this work. This represents a
significant departure from existing MRAC systems, where the estimation error
equation is typically in a bilinear regression form. The linear regression form
facilitates the direct estimation of all unknown parameters, thereby
simplifying the adaptive control process. The proposed method preserves
closed-loop stability and ensures asymptotic output tracking, overcoming some
of the limitations associated with existing methods like Nussbaum and
multiple-model based methods. The practical efficacy of the developed MRAC
method is demonstrated through detailed simulation results within an aircraft
control system scenario.
