Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 56, Issue 3, Pages 637-643Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2010.2091187
Keywords
Multiple-input multiple-output (MIMO)
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Compensation of infinite-dimensional input or sensor dynamics in SISO, LTI systems is achieved using the backstepping method. For MIMO, LTI systems with distributed input or sensor dynamics, governed by diffusion with counter-convection, we develop a methodology for constructing control laws and observers that compensate the infinite- dimensional actuator or sensor dynamics. The explicit construction of the compensators are based on novel transformations, which can be considered of backstepping-forwarding type, of the finite-dimensional state of the plant and of the infinite-dimensional actuator or sensor states. Based on these transformations we construct explicit Lyapunov functionals which prove exponential stability of the closed-loop system, or convergence of the estimation error in the case of observer design. Finally, we illustrate the effectiveness of our controller with a numerical example.
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