Construction of Worst-Case Input Signals for Discrete-Time Linear Time-Varying Systems

This paper provides two algorithms for constructing worst-case input signals that have finite support and approximately achieve the induced gain of a stable, discrete-time, linear time-varying system. The focus of this work is on eventually periodic systems, which include finite horizon and periodic systems, and so the results can be immediately specialized for these systems. Novel results on the Riccati Difference Equations for eventually periodic systems are provided and utilized in one of the algorithms. The utility and effectiveness of the proposed algorithms are demonstrated in an illustrative example.