LAUSR

The problem of mixed $$H_{\infty }$$ and passivity performance analysis is investigated for interfered digital filters under Markovian jumping parameters, time-varying delays and various combinations of quantization and overflow nonlinearities. By virtue of Lyapunov–Krasovskii stability approach, a novel sufficient condition is derived such that the underlying system is stochastically stable and satisfies a prescribed mixed $$H_{\infty }$$ and passivity performance index. In a unified framework, the proposed criterion can be used for the $$H_{\infty }$$ performance, the passivity and the mixed $$H_{\infty }$$ and passivity performance of digital filters. Moreover, the problem is formulated to obtain optimal performance index (i.e. $$H_{\infty } ,$$ passivity and mixed $$H_{\infty }$$ and passivity) of interfered digital filters. At last, two numerical examples and an interfered digital filter with tridiagonal state-space model are applied to demonstrate the effectiveness of the proposed approach.