Block-form control of linear time-invariant discrete-time systems defined over commutative rings

AbstractA new approach based on a block-input, block-output state model is developed for the study of linear time-invariant discrete-time systems whose coefficients belong to a commutative ring with 1. It is well known that such systems arise in the study of various classes of complex linear systems including systems depending on parameters and multidimentional systems. By time-compressing the block-input state representation, new results are obtained on the construction of a memoryless block-form state feedback control law that yields a type of assignability and/or deadbeat control. These results are then dualized to yield results on a new type of state observer based on a block of output measurements. The observer and state feedback controller are then combined to yield new results on input-output regulation and set-point tracking for systems defined over an arbitrary commutative ring. In the last part of the paper, the block-input form is utilized to study the stabilization of systems defined over a normed algebra