Adaptive stabilization of non-necessarily inversely stable first-order continuous-time systems without using a hysteresis switching function

This paper presents a an adaptive control scheme for first-order continuous-time systems which is free from singularities. The singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That property is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold