Robust stability analysis based on noncausal LPTV FIR scaling: Explicit procedure and relationship with causal LTI FIR scaling

This paper develops a framework of a robust stability analysis approach called discrete-time noncausal linear periodically time-varying (LPTV) finite impulse response (FIR) scaling. This approach is an extension of (frequency-dependent) causal linear time-invariant FIR scaling, obtained by further introducing time dependence through lifting treatment. This paper first provides a theoretical result showing how such newly introduced time dependence contributes to reduction of conservativeness of robust stability analysis. We further provide linear matrix inequality conditions for robust stability and develop an explicit and feasible numerical method by exploiting noncausal LPTV FIR scaling. The effectiveness of this scaling approach is demonstrated and the above theoretical result is confirmed through numerical examples.