On necessary conditions of instability and design of destabilizing controls

The problem of formulation of an equivalent characterization for instability is considered. The necessary part of the Chetaev´s theorem on instability is formulated. Using the developed necessary instability conditions, the Anti-control Lyapunov Function (ALF) framework from [1] is extended and the Control Chetaev Function (CCF) concept is proposed as a counterpart of the Control Lyapunov function (CLF) theory. A (bounded) control is designed, which destabilizes a nonlinear system based on CCF, this control design approach can be useful either for generation of an oscillating or chaotic behavior as in [1], or for analysis of norm controllability from [2].