Quadratic stabilisation with H∞-norm bound of non-linear discrete-time uncertain systems with bounded control

The paper addresses the problem of quadratic stabilisability with H_∞-norm bound of uncertain discrete-time control-affine systems by norm-bounded controls. Both structured parameter uncertainties and unstructured exogenous disturbances are taken into account. The given definition of quadratic stabilisability is a generalisation of that used for linear systems so far. A necessary condition of the stabilisability is formulated. A state feedback control satisfying an a priori constraint is proposed for the solution of the formulated H_∞ problem. The proposed method may be applicable even in such cases when the linearisation technique cannot be used.