A framework for system analysis and design is described based on nonlinear system models and nonperiodic signals generated by nonlinear systems. The proposed approach to analysis of nonlinear systems is based on an excitability index-a nonlinear counterpart of the magnitude frequency response of linear systems. It can be used for stability analysis of fully nonlinear cascade systems similarly to absolute stability analysis of Lur'e systems. Speed-gradient algorithms of creating feedback resonance in nonlinear multi-DOF oscillators are described. For strictly dissipative systems bounds of energy and excitability change by feedback are established.