Stability of digital filters subject to external interference and state-delay

This paper presents passivity-based results to address stability of interfered digital filters with state-delay and saturation nonlinearities. A very-strict passivity condition is proposed for the digital filters by using an appropriate Lyapunov-Krasovskii functional. The established criterion ensures limit-cycle free realization of state-delayed interfered digital filters using saturation arithmetic. Conditions for passivity, input-strict passivity and output-strict passivity of the digital filters are obtained as special cases of the proposed result. In addition, an asymptotic stability condition for the digital filters with zero external interference is presented. It is also demonstrated that a stability condition reported in a recent work may be recovered from the established criterion. Numerical simulations are given to demonstrate worthiness of the proposed results.

Overflow oscillations free implementation of state-delayed digital filter with saturation arithmetic and external disturbance

This paper presents a sufficient condition for exponential stability and confirms [Formula: see text] performance of state-delayed digital filters in the simultaneous existence of saturation arithmetic and external disturbance. The realization of limit-cycle free state-space digital filters is carried out by utilizing better characterization of saturation nonlinearities. The presented criterion not only ensures exponential stability but also reduces effect of external interference to a specific attenuation level. The obtained condition is in linear matrix inequality framework, so it is easily tractable. It is also shown that many results reported in literature may be retrieved as a special case from the proposed condition. With the help of numerical examples, it is shown that the presented approach provides enhanced stability region for the digital filters as compared to an existing criterion appeared in literature.

Passivity Based Stability Condition for Interefered Digital Filters

This paper presents a new passivity condition for fixed-point state-space interfered digital filters using saturation arithmetic. Passivity is a way to characterize input-output stability of a system, that is, supplied bounded input energy produces bounded output energy. The presented criterion also ensures asymptotic stability of the state-space digital filter with zero external disturbances. The result is expressed in terms of linear matrix inequality, and therefore, can be solved via existing numerical packages. A numerical example is arranged to validate the usefulness of the proposed method.

An Improved Criterion for Induced Stability of Fixed-Point Digital Filters with Saturation Arithmetic

<p>This paper establishes a criterion for the induced stability of fixed-point state-space digital filters with saturation nonlinearities and external interference. The criterion is established in a linear matrix inequality (LMI) setting, and therefore, computationally tractable. The criterion turns out to be an improvement over a previously reported criterion. A comparison of the presented criterion with existing criterion is made. Numerical examples are given to demonstrate the usefulness of the proposed approach.</p>