Generalized state scaling-based robust control of nonlinear systems and applications to triangular systems

In this paper, we propose a high-gain scaling based controller to achieve global state-feedback stabilization of a general class of nonlinear systems which are allowed to contain uncertain functions of all the states and the control input as long as polynomial bounds on ratios of some uncertain system terms are available. The design is based on a high-gain scaling involving appropriate powers of a high-gain scaling parameter which is a dynamic signal driven by the state. The designed controller has a very simple structure being essentially a dynamic extension and a linear feedback with state-dependent dynamic gains. The obtained results are applicable to both lower triangular (strict-feedback) and upper triangular (feedforward) structures and also to systems without any triangular structure as long as a set of inequalities involving powers of the polynomial bounds on the ratios of the uncertain system terms and scaling orders is solvable. The stability analysis is based on our recent results on uniform solvability of coupled state-dependent Lyapunov equations.