Stabilization of Triangular Nonlinear Systems With Multiplicative Stochastic State Sensing Noise
Wuquan Li, Miroslav Krstić
Abstract
We present new state feedback control designs for lower/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 the 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.