Exponential Stability of Gradient Systems with Applications to Nonlinear-in-Control Design Methods

Exponential stability analysis for gradient systems is the primary focus of this paper. Sufficient conditions are derived that guarantee exponential stability for both autonomous and parameter-dependent gradient systems. These conditions require boundedness of singular values of a Jacobian matrix, uniformly in the system state space. The reported theoretical results are subsequently applied to design tracking controllers for a class of nonlinear-in-control dynamical systems. The design is carried out using time-scale separation techniques.