Sector bounds in control design and analysis

The Sector Stability Theorem is an intuitive condition for the stability of feedback loops that unifies many lines of research including robust control, passivity theory, dissipativity theory, and integral quadratic constraints (IQC) theory. This theorem plays a central role in deriving a frequency-domain test for general sector bounds and is used to develop efficient numerical algorithms for checking and enforcing sector bounds on linear time-invariant (LTI) systems. The notion of relative and directional indices are also developed. Two application examples illustrate the potential of the tool and techniques discussed in the paper.