New ISS Result for Lipschitz Nonlinear Interfered Digital Filters Under Various Concatenations of Quantization and Overf
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New ISS Result for Lipschitz Nonlinear Interfered Digital Filters Under Various Concatenations of Quantization and Overflow Janmejaya Rout1
· Haranath Kar1
Received: 13 November 2019 / Revised: 24 September 2020 / Accepted: 26 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper establishes a new input-to-state stability (ISS) criterion for Lipschitz nonlinear discrete systems with external disturbance and finite register length nonlinearities. The finite register length nonlinearities comprise of different concatenations of quantization and overflow nonlinearities commonly produced in practice during the hardware realization of the discrete systems. The new ISS criterion can be utilized to affirm the diminishing consequence of external disturbance and to ensure whether the nonlinear system with zero disturbance is asymptotically stable. The utility of the criterion is demonstrated with the help of several examples. Keywords Digital filter · External disturbance · Input-to-state stability · Lipschitz nonlinear system · Overflow arithmetic · Quantization nonlinearity
1 Introduction Over the last decades, digital filters have found extensive applications in telecommunications, speech processing, image processing, control and navigation systems etc. [9, 12, 41, 42]. In the hardware implementation of recursive linear digital filters on fixed-point finite register length digital signal processors like digital signal processing (DSP) kits, microcontrollers, field-programmable gate arrays (FPGAs), quantization and overflow nonlinearities are normally introduced [17, 21]. Magnitude truncation (MT), 2 s complement truncation and rounding are commonly used quantization mechanisms in digital filters. Saturation, 2 s complement, zeroing and triangular overflow
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Janmejaya Rout [email protected] Haranath Kar [email protected]
1
Department of Electronics and Communication Engineering, Motilal Nehru National Institute of Technology Allahabad, Prayagraj 211004, India
Circuits, Systems, and Signal Processing
correction schemes are frequently employed in digital filters to tackle the overflow. In presence of finite register length nonlinearities, digital filters may display unstable behavior in the form of granular limit cycles, overflow oscillations, etc. [17, 21, 25]. The stability problem of digital filters involving quantization effects has been studied in [13–15, 20] by neglecting the effects of overflow. Under the assumption that quantization effects are negligible, many researchers have investigated the effects of overflow on digital filters [30, 31, 37]. In practice, the practical digital filters usually operate under different concatenations of quantization and overflow nonlinearities. Therefore, the investigation of stability behavior of such filters appears to be more realistic [1, 24, 28, 29, 35]. External disturbances frequently corrupt the physical systems. The realization of an nth-order (n > 2) digital filter using a number of low-order filte
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