Control of Linear Systems Over Commutative Normed Algebras with Applications

摘要

The research centered on the development of a control theory for various classes of complex linear systems, including systems with time delays, systems with unknown parameters and time-varying systems. In the work on systems with time delays, we have been able to prove that stabilizable systems with one or more noncommensurate time delays can always be stabilized using a lumped (finite-dimensional) compensator. In many cases of interest such as delays in control or delays in measurements, we have developed explicit constructive procedures for designing lumped compensators. In the work on systems with unknown parameters, we have developed an indirect adaptive control scheme that does not require a persistent excitation to achieve global stability. The scheme is based on a new parameter estimation algorithm that forces the estimates of the unknown system parameters to converge to pre-specified intervals. In the work on linear time-varying systems, we have developed a new approach to control based on a type of system augmentation. Via this approach, we have derived a number of results on the existence of canonical forms such as the control canonical form. We have also developed a 'pole-placement' algorithm for time-varying systems. (Author)