Mixed disturbance action for stabilized control systems (necessary conditions)

It is shown that the impulsive (generalized) systems can be combined with usual bang-bang disturbance systems to yield mixed disturbance action systems. The state response is governed by nonlinear differential equations with bounded disturbance action ω and impulse disturbance action υ. The impulse disturbance action has its structure given that is affine υ=Σ_i=1^k c_iδ(t-t_i), |c_i|⩽1. In this case the differential equation solution is a discontinuous function. After changing the original task into k+1 auxiliary combined degrading severity tasks, we get the necessary conditions for the most stressful disturbance of mixed action for some stable systems. Examples are given to illustrate the theory