Modified circle criterion of absolute stability and robustness estimation

Stability Metric Based on Sensitivity Analysis Applied to Electrical Repowering System

“…The higher the number of scenarios in a certain range, the greater the stability of this operating range. Chestnov and Shatov [12] propose similar reasoning, suggesting that the limits were the system's input parameters can vary between so that their outputs maintain equilibrium, determine their stability margins. The methodology proposed by Pesterev [13] also allows identifying stable operating intervals of the system, called stability sectors.…”

Output feedback robust stabilisation for uncertain non‐linear systems with dead‐zone input

“…To deal with system uncertainties, the absolute stability theory was proposed and used extensively, as the first robust stability theory [4]. The classical circle criterion is its theoretical basis, which is used to prove the absolute stability of the linear optimal control systems having entered sectoral non‐linearities (see, for example, [5, 6]). Actuator dead‐zone non‐linearity, as a class of important non‐smooth non‐linearities, often occur in lots of practical systems such as upper‐limb model, ultrasonic motor and servo‐valve, as shown in [7].…”