Finite-timeH_∞filtering for non-linear stochastic systems

Abstract

This paper describes the robust H ∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H ∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H ∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

Finite-time event-triggered control for stochastic systems with multiple disturbances

“…13–17 In the last few years, finite-time anti-disturbance control has developed rapidly. 18–20 In the work of Zhang et al, 18 a new finite-time controller was constructed for the nonlinear system, which guarantees globally finite-time stable. In the work of Hou et al, 19 combining with H ∞ filtering control to attenuate disturbance, finite-time bounded was achieved for nonlinear stochastic systems with exogenous disturbance.…”

“…18–20 In the work of Zhang et al, 18 a new finite-time controller was constructed for the nonlinear system, which guarantees globally finite-time stable. In the work of Hou et al, 19 combining with H ∞ filtering control to attenuate disturbance, finite-time bounded was achieved for nonlinear stochastic systems with exogenous disturbance. In the work of Zhang et al, 20 H ∞ control technique was applied to the Markov jumping system to restrain the bounded disturbance.…”

Finite‐time stabilization of stochastic low‐order nonlinear systems with FT‐SISS inverse dynamics

“…Based on this definition and stability theorem, Khoo et al() and Gao and Yuan solved finite‐time stabilization problem for some kinds of stochastic nonlinear systems. The finite‐time filtering problems for different stochastic nonlinear systems were studied by Hou et al and Luan et al() Wang and Zhu and Lan et al studied finite‐time stabilizers for stochastic high‐order systems. All of these works are under the assumption of z =0 and the system order r i =1( i =1,…, n ) or r i ≥1.…”