A Sufficient Condition for Invalidation of Linear State-Space Systems With Uncertain Time-Varying Parameters

The model validation problem for linear systems with time-varying parameter uncertainty and additive disturbances is addressed. The disturbance are modelled using the window norm, which is a generalization of the ${rm l}_{infty}$-norm and is shown to be attractive for optimal control. An approximation of the nonlinear operator from parameters to output is found based on the FrÉchet derivative. Using this approximation, a sufficient condition for invalidation of a process model is formulated as a linear feasibility problem. In this condition, an upper bound for the approximation error is included. An overhead crane is used as an illustrative example to show that the model validation test is realistic to perform even with large data sets.