Adaptive stabilization of non-necessarily inversely stable first-order systems by using estimates modification based on testing the Sylvester determinant
This paper presents an algorithms for adaptive stabilization of first-order continuous time systems with a zero that can be stable or unstable. Parameter modification of only one parameter is used by the adaptive scheme. Neither hysteresis switching nor reliance on the properties of the covariance matrix are required. Instead, singularities are avoided through a modification of the a priori estimated plant parameters so that the associated Sylvester matrix is guaranteed to be nonsingular. Nonsingularity is achieved by insuring that the absolute value of the determinant of the Sylvester matrix exceeds a positive threshold. The author first provides the adaptive stabilization results for the nominal plant and proves the global asymptotic stability of the closed-loop system. The results are then extended to the case where plant uncertainties are present in the form of bounded noise and a standard class of unmodelled dynamics. Global stability of the scheme is again established. Some brief comments about extensions of this approach to second-order systems are also provided.
scientific article; zbMATH DE number 1981451
scientific article