a b s t r a c tRepetitive processes are a class of 2D systems that operate over a subset of the upper-right quadrant of the 2D plane. Applications include iterative learning control where experimental verification has been reported based on a linear time-invariant model approximation of the dynamics. This paper considers discrete nonlinear repetitive processes with Markovian switching and applies, as one application, the resulting stability theory to iterative learning control for a class of networked systems where time-varying dynamics arise.

Repetitive processes are characterized by repeated executions of a task defined over a finite duration with resetting after each execution is complete. Also the output from any execution directly influences the output produced on the next execution. The repetitive process model structure arises in the modeling of physical processes and can also be used to effect in the control of other systems, such as iterative learning control where experimental verification of designs has been reported. The existing systems theory for them is, in the main, linear model based. This paper considers nonlinear repetitive processes using a dissipative setting and develops a stabilizing control law with the required conditions expressed in terms of vector storage functions. This design is then extended to stabilization plus disturbance attenuation.

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