System Analysis via Integral Quadratic Constraints. Part II

In this second report on system analysis via integral quadratic constraints, the theory is refined compared to Part I [6], to cover a number of additional cases. The report is split into two halfs, denoted Part IIa and Part IIb. Unbounded operators are treated by encapsulating them in a feedback loop, that has bounded closed loop gain. A general theorem for well-posedness of such feedback loops is given. A concept of “fading memory” is introduced and plays an important role in the study of exponential stability. It is also shown how system performance can be studied with restrictions on the class of input signals. In particular, for sinusodal inputs, we compute bounds on high order harmonics in the system response.