ADAPTIVE STABILIZATION USING A VARIABLE SAMPLING RATE

It is observed that digital versions of globally stable adaptive stabi lization algorithms are, at best, locally stable due to incompatibilit ies between the gain adaptation algorithms and the choice of sampling rate. This fact suggests the problem of retrieving global asymptotic s tability for such difficulties by modifications to the stabilization a lgorithms to include sampling rates as control variables and the inclu sion of extra plant information to relate sampling rates to gain evolu tions. In this contribution, the theoretical problem of adaptive stabi lization of single-input single-output (SISO) linear systems S(A, B, C ) in R(n) is approached using the sampling rate as the basic adaptive mechanism. A wide range of sample interval adaptation schemes is deriv ed that guarantees global asymptotic stability of the sampled outputs from the plant for any minimum-phase SISO systems satisfying the relat ive degree one constraint CB not equal 0. The control laws are 'univer sal' in the sense that stabilization is achieved despite a lack of kno wledge of the systems parameters and state dimension. They also guaran tee the stability of the underlying continuous system's state response if either the system has no open-loop oscillatory unstable poles or i t is under a sufficiently fast initial choice of sampling interval, or for any other generically chosen sample interval.