Adaptive stabilization using a variable sampling rate

Abstract

It is observed that digital versions of globally stable adaptive stabilization algorithms are, at best, locally stable due to incompatibilities between the gain adaptation algorithms and the choice of sampling rate. This fact suggests the problem of retrieving global asymptotic stability for such difficulties by modifications to the stabilization algorithms to include sampling rates as control variables and the inclusion of extra plant information to relate sampling rates to gain evolutions. In this contribution, the theoretical problem of adaptive stabilization of single-input single-output (SISO) linear systems S(A,B, C) in Rnis approached using the sampling rate as the basic adaptive mechanism, A wide range of sample interval adaptation schemes is derived that guarantees global asymptotic stability of the sampled outputs from the plant for any minimum-phase SISO systems satisfying the relative degree one constraint CB ≠ 0. The control laws are ‘universal’ in the sense that stabilization is achieved des...