arXiv subjects

Bor-Sen Chen

Publications and source records attributed to Bor-Sen Chen.

4 recordsLinked to original sources

arXiv2023

On stabilizability and exact observability of stochastic systems with their applications

This paper discusses the stabilizability, weak stabilizability, exact observability and robust quadratic stabilizability of linear stochastic control systems. By means of the spectrum technique of the generalized Lyapunov operator, a necessary and sufficient condition is given for stabilizability and weak stabilizability of stochastic systems, respectively. Some new concepts called unremovable spectrums, strong solutions, and weakly feedback stabilizing solutions are introduced. An unremovable spectrum theorem is given, which generalizes the corresponding theorem of deterministic systems to stochastic systems. A stochastic Popov-Belevith-Hautus (PBH) criterion for exact observability is obtained. For applications, we give a comparison theorem for generalized algebraic Riccati equations (GAREs), and two results on Lyapunov-type equations are obtained, which improve the previous works. Finally, we also discuss robust quadratic stabilization of uncertain stochastic systems, and a necessary and sufficient condition is given for quadratic stabilization via a linear matrix inequality (LMI).

math.OC↗

arXiv2018

Mixed $H_-/H_{\infty}$ Fault Detection Filtering for Itô-Type Affine Nonlinear Stochastic Systems

This paper studies the mixed $H_-/H_{\infty}$ fault detection filtering of Itô-type nonlinear stochastic systems. Mixed $H_-/H_{\infty}$ filtering combines the system robustness to the external disturbance and the sensitivity to the fault of the residual signal. Firstly, for Itô-type affine nonlinear stochastic systems, some sufficient criteria are obtained for the existence of $H_-/H_{\infty}$ filter in terms of Hamilton-Jacobi inequalities (HJIs). Secondly, for a class of quasi-linear Itô systems, a sufficient condition is given for the existence of $H_-/H_{\infty}$ filter by means of linear matrix inequalities (LMIs). Finally, a numerical example is presented to illustrate the effectiveness of the proposed results.

math.OC↗

arXiv2017

New Approach to General Nonlinear Discrete-Time Stochastic $H_\infty$ Control

In this paper, a new approach based on convex analysis is introduced to solve the $H_\infty$ problem for discrete-time nonlinear stochastic systems. A stochastic version of bounded real lemma is proved and the state feedback $H_\infty$ control is studied. Two examples are presented to show the effectiveness of our developed theory.

math.OC↗

arXiv2015

Detectability, Observability and Lyapunov-Type Theorems of Linear Discrete Time-Varying Stochastic Systems with Multiplicative Noise

The objective of this paper is to study detectability, observability and related Lyapunov-type theorems of linear discrete-time time-varying stochastic systems with multiplicative noise. Some new concepts such as uniform detectability, ${\cal K}^{\infty}$-exact detectability (resp. ${\cal K}^{WFT}$-exact detectability, ${\cal K}^{FT}$-exact detectability, ${\cal K}^{N}$-exact detectability) and ${\cal K}^{\infty}$-exact observability (resp. ${\cal K}^{WFT}$-exact observability, ${\cal K}^{FT}$-exact observability, ${\cal K}^{N}$-exact observability) are introduced, respectively, and nice properties associated with uniform detectability, exact detectability and exact observability are also obtained. Moreover, some Lyapunov-type theorems associated with generalized Lyapunov equations and exponential stability in mean square sense are presented under uniform detectability, ${\cal K}^{N}$-exact observability and ${\cal K}^{N}$-exact detectability, respectively.

math.OC↗