This paper analyzes the dissipativity of the direct form digital filters with saturation nonlinearity. First a (Q,S,R)-α dissipativity of direct form digital filters with saturation nonlinearity has been studied. Based on this existing criterion a new (Q,S,R)-α dissipativity criterion of direct form digital filters has been established and verified with some general characterization of nonlinearity.
This paper also deals under what conditions the asymptotic stability of the digital filters can be assured which is very crucial for the design of robust controllers. Some numerical examples have been employed to demonstrate the usefulness of the theorems. The theorems in this paper have been verified using the suitable Lyapunov and dissipative functions.
dissipativity, digital filters, direct form, Lyapunov
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