Stabilization of Triangular Nonlinear Systems With Multiplicative Stochastic State Sensing Noise

Abstract

We present new state-feedback control designs for lower-triangular/upper-triangular nonlinear systems with multiplicative stochastic sensor uncertainty. For lower-triangular nonlinear systems with small sensor noise, we develop a novel control design where the control gains are suitably constructed to simultaneously dominate the nonlinear functions and sensor noise of sufficiently small multiplicative gain. For upper-triangular nonlinear systems, we propose a new low-gain domination design, the advantage of which is that it can effectively deal with the sensor noise with arbitrarily large intensities. These two designs can both ensure that closed-loop system has an almost surely unique global solution, the origin of the closed-loop system is mean-square stable, and the states can be regulated to zero almost surely. Finally, two simulation examples are given to illustrate the designs.