Parametric quadratic stabilizability of uncertain nonlinear systems
This paper deals with the problem of parametric quadratic stabilizability of nonlinear systems of the Lure-Postnikov type: \[ x'= [A+ \Delta A(p)]x+ [B+ \Delta B(p)] \mu(u), \] where \(p\) is the parameter vector and \(\mu(u)\) is a nonlinear function. When the system is linear, a number of powerful results related to \(Q\)-stabilizability are available. However, in these cases, it is assumed that the equilibrium of the uncertain system remains fixed in the origin despite the parametric and input disturbances. When a system is nonlinear as in the case considered in the paper, reference inputs and disturbances may alter the dynamics of the system in an essential way, by moving the equilibrium to a new location, or even destroying it. Thus, the results provided are a significant generalization of the previous theory. In particular, under assumptions on the nonlinearity, necessary and sufficient conditions for stabilizability of the system under linear static or dynamic state feedback are given.
scientific article; zbMATH DE number 612404