Mixed FTS/H∞ Control for Nonlinear Quadratic Systems Subject to Norm-Bounded Disturbances

In this paper, the mixed Finite-Time Stability (FTS)/$\mathscr{H}_{\infty}$ control problem is investigated for the class of nonlinear quadratic systems (NLQSs), which have several relevant applications, e.g., in robotics, systems biology and other domains of applied sciences. Sufficient conditions are provided here to solve synthesis problems, in the presence of both norm-bounded disturbances, constraints on initial and terminal conditions, and finite-time bounds on the output transient. More specifically, taking into account such constraints within the design phase, allows to achieve a desired $\mathscr{H}_{\infty}$ performance with nonzero initial conditions, while simultaneously guaranteeing that a given NLQS is finite-time stable for all admissible uncertainties and disturbances. Such conditions can be formulated as Linear Matrix Inequalities (LMIs) optimization problem. The applicability of the proposed results is illustrated by means of a numerical example.