Interval Homogeneity-Based Control for a Class of Nonlinear Systems With Unknown Power Drifts

Abstract

This note considers the global stabilization problem for a class of nonlinear systems with unknown power (exponent) drifts. Based on the concept of interval homogeneity with monotone degrees, the allowable bounds of the unknown power drifts can be explicitly determined to guarantee the solvability of the problem. The technique of adding a power integrator is revamped based on a new Lyapunov function with interval parameters and is recursively employed to construct a global stabilizer for the nonlinear systems.Index Terms-Global stabilization, p-normal form, unknown power drift, interval homogeneity, adding a power integrator

Smooth output feedback stabilization for a class of nonlinear systems with time‐varying powers

“…This paper aims to investigate the aforementioned question and give a constructive approach to design a smooth controller. Compared with the existing results , the main obstacles lie in three aspects: (i) the approaches of are based on the adding a power integrator technique; therefore, their design procedures are no longer workable for stabilizing controller design of system because Lyapunov functions used in will inescapably involve the time‐varying powers. (ii) The method presented in is inapplicable to system because the power considered in is required to be an unknown constant belonging in a known real interval.…”

“…Specifically, [6][7][8][9] investigated the case when the power p.t/ D 1, and [10][11][12][13][14][15][16][17] focused on the case of p.t/ D constant > 1, with the aid of adding a power integrator technique and recursive observer design. Recently, the work in [4] developed an interval homogeneity-based control scheme to solve the global state feedback stabilization problem of systems (1) under the assumption that the power is an unknown constant in a known real interval. Note that a common assumption of the existing results [4,[10][11][12][13][14][15][16][17] is that powers must be a constant.…”

“…Recently, the work in [4] developed an interval homogeneity-based control scheme to solve the global state feedback stabilization problem of systems (1) under the assumption that the power is an unknown constant in a known real interval. Note that a common assumption of the existing results [4,[10][11][12][13][14][15][16][17] is that powers must be a constant. Therefore, from theoretical point of view, an interesting question is naturally proposed: Can we find a state/output feedback controller to globally stabilize system (1) in which the power is varying with time?…”

“…This paper aims to investigate the aforementioned question and give a constructive approach to design a smooth controller. Compared with the existing results [4,[11][12][13][14][15][16][17], the main obstacles lie in three aspects: (i) the approaches of [11][12][13][14][15][16][17] are based on the adding a power integrator technique; therefore, their design procedures are no longer workable for stabilizing controller design of system (1) because Lyapunov functions used in [11][12][13][14][15][16][17] will inescapably involve the time-varying powers.…”

“…(ii) The method presented in [4] is inapplicable to system (1) because the power considered in [4] is required to be an unknown constant belonging in a known real interval. (iii) With time-varying powers, the system (1) is intrinsically time-varying and more complicated.…”