On the Nonlinear Stabilization Problem via Quadratic Immersion Part II: A QI-based approach for the design of nonlinear regulators having exponential-tunable performance

The results of Part I of the paper are here exploited in order to define a regulator design method for Sigma/Pi-systems, even non stationary, which makes use of a static state-feedback working in the same domain as the open-loop system. Sufficient conditions are given in order that a fixed performance, in terms of convergence rate, be achievable. Provided these conditions are satisfied the regulator steers the system state to zero, at an exponential, tunable, rate and the domain of 'attraction' of the zero will include all points from which the orbits of the closed-loop system are bounded. For stationary systems additional results are proven as far as the accessibility property.