Homogeneous Domination Control for Uncertain Nonlinear Systems via Interval Homogeneity With Monotone Degrees

It is challenging and interesting to globally stabilize the
$p$
–normal form nonlinear system with unknown power integrators. The most difficulty arising from the unknown power integrators is that the power integrator drift causes uncertain homogeneity as well as unknown parameters in Lyapunov function. This paper revamps the tool of adding a power integrator to recursively construct a state-dependent homogeneous domination stabilizer for the
$p$
–normal form system with interval power integrators based on the new concept of interval homogeneity with monotone degrees. To judge the existence of interval homogeneity with monotone degrees, a so-called admissible index is proposed. We show that if the system has positive admissible index(es) then it has interval homogeneity with monotone degrees and the interval homogeneity as well as homogeneous weights can be calculated by a rule. Both theoretical analysis and simulations validate our method and conclusions.