Delay-Integral-Quadratic Constraints and Stability Multipliers for Systems With MIMO Nonlinearities

The formula for stability multipliers for systems with MIMO nonlinearities is derived using the method of delay-integral-quadratic constraints. The results, applicable to both time-invariant and time-periodic systems, are then used to derive a solution for a special case of a nonlinear regulation problem and a criterion for stability of forced oscillations. A linear time-periodic system is considered to illustrate the difference between the delay-integral-quadratic constraints that yield stability criteria in multiplier form and those that do not.