A State-Space Approach to Parametrization of Stabilizing Controllers for Nonlinear Systems

A state-space approach to Youla-parametrization of stabilizing controllers for linear and nonlinear systems is suggested. The stabilizing controllers (or a class of stabilizing controllers for nonlinear systems) are characterized as (linear/nonlinear) fractional transformations of stable parameters. The main idea behind this approach is to decompose the output feedback stabilization problem into state feedback and state estimation problems. The parametrized output feedback controllers have separation structures. A separation principle follows from the construction. This machinery allows the parametrization of stabilizing controllers to be conducted directly in state space without using coprime-factorization

Input-Output-to-State Stability

This work explores Lyapunov characterizations of the input-output-to-state stability (IOSS) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zero-detectability property used in the linear case. The main contribution of this work is to establish a complete equivalence between the input-output-to-state stability property and the existence of a certain type of smooth Lyapunov function. As corollaries, one shows the existence of ``norm-estimators'', and obtains characterizations of nonlinear detectability in terms of relative stability and of finite-energy estimates.Comment: Many related papers can be found in: http://www.math.rutgers.edu/~sonta