Generalized Gap Metrics and Robust Stability of Nonlinear Systems.
Communication in Applied Analysis (to appear)
A gap metric of Georgiou and Smith (IEEE Trans. Auto. Control, 42(9):1200--1229, 1997), which does not need causal and surjective mapping between graphs to define, is studied and generalized based on the notion of biased norm, the corresponding robust stability theorem is presented in the notion of stability with bias terms. The obtained results are then applied to studied the stability of linear system realizations, semilinear systems with bounded nonlinearities and a nonlinear system with time delay in the inputs.
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