Sufficient LMI conditions and Lyapunov redesign for the robust stability of a class of feedback linearized dynamical systems

The robust stability of a class of feedback linearizable minimum-phase nonlinear system, having parametric uncertainties, is investigated in this study. The system in new coordinates is represented to an equivalent formulation after the attempt of feedback linearization. Due to the parametric uncertainties the approximately linearized system entails a norm bounded input nonlinearity such that the equilibrium point condition in error dynamics can not be satisfied. Accordingly, to guarantee the regional asymptotic stability a control synthesis problem is proposed by means of sufficient Linear Matrix Inequalities (LMIs) together with an amended nonlinear control term, derived from the Lyapunov redesign method, which tackles zero steady-state error condition. The numerical examples of a general aviation aircraft's longitudinal dynamics and inverted pendulum are simulated to show the proficiency of the proposed control technique.