zbMATH — the first resource for mathematics

Arbitrary adaptive pole placement for linear multivariable systems. (English) Zbl 0534.93026
The authors present a method for assigning all the closed-loop poles of a linear time-invariant multivariable system. The approach is applicable to the complete class of continuous-time multivariable systems characterized by proper transfer matrices. Required a priori information for implementation consists of only the system controllability indexes and an upper bound on the observability indexes. In the presentation, both the continuous-time and the discrete-time case are treated almost in parallel. At first, a fixed control strategy is formulated which can be interpreted as linear state feedback via asymptotic state estimation. Then the adaptive control strategy is developed, which may be implemented by a state space realization of order (dim. of input vector)\(\times\)(upper bound of the observability indexes). Local stability results are mentioned. In the last section, three instructive examples are treated in detail.
Reviewer: A.Munack

93B55 Pole and zero placement problems
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
93C40 Adaptive control/observation systems
93C55 Discrete-time control/observation systems
93C99 Model systems in control theory
Full Text: DOI