Neo-robust control theory (part I)

The celebrated small-gain approach to robust control only makes use of the gain information of uncertainty. This results in a limitation on the achievable control bandwidth in system design. On the other hand, the alternative passivity approach has only limited applications. To relax the limitations associated with small-gain and passivity approaches, we explore the possibility of utilizing both the gain and the phase information of uncertainty in robust control design. The modelling of uncertainty accounting for both gain and phase is discussed first. Then conditions for the robust stability are derived. These conditions are described as either phase or gain constraints on the nominal system in finite frequency bands. Finally, it is revealed, both theoretically and via a HDD benchmark, that by using the phase information of uncertainty, much higher robust performance can be achieved than the existing small-gain and passivity approaches.