  In this paper, we consider the analysis and control of continuous-time
nonlinear systems to ensure universal shifted stability and performance, i.e.,
stability and performance w.r.t. each forced equilibrium point of the system.
This "equilibrium-free" concept is especially beneficial for control problems
that require the tracking of setpoints and rejection of persistent
disturbances, such as input loads. In this paper, we show how the velocity
form, i.e., the time-differentiated dynamics of the system, plays a crucial
role in characterizing these properties and how the analysis of it can be
solved by the application of Linear Parameter-Varying (LPV) methods in a
computationally efficient manner. Furthermore, by leveraging the properties of
the velocity form and the LPV framework, a novel controller synthesis method is
presented which ensures closed-loop universal shifted stability and
performance. The proposed controller design is verified in a simulation study
and also experimentally on a real system. Additionally, we compare the proposed
method to a standard LPV control design, demonstrating the improved stability
and performance guarantees of the new approach.
