Phan Thanh Nam

Hieu Trinh, Phan Thanh Nam, Tran Ngoc Nguyen

This paper investigates the stabilization of linear systems subject to simultaneous, mismatched time delays in both the control input and system output vectors. The proposed control framework is developed in two primary stages. First, an asymptotically stabilizing delayed state-feedback controller is synthesized by leveraging recent advancements in Linear Matrix Inequality (LMI) techniques. Second, this controller is realized using novel time-delay compensators \cite{trinhnam26}. This architecture successfully accommodates an output measurement delay $τ_y$ that is independent of the input delay $τ_u$, enabling direct estimation of the delayed state-feedback control law. The proposed methodology is then extended to target output controllers to account for simultaneous, mismatched time delays in both the control input and system output vectors.

Dang Duc Trong, Phan Thanh Nam, Phung Trong Thuc

Let a three-dimensional isotropic elastic body be described by the Lamé system with the body force of the form $F(x,t)=ϕ(t)f(x)$, where $ϕ$ is known. We consider the problem of determining the unknown spatial term $f(x)$ of the body force where the surface stress history is given as the overdetermination. This inverse problem is ill-posed. Using the interpolation method and truncated Fourier series, we construct a regularized solution from approximate data and provide explicit error estimates. AMS 2010 Subject Classification: 35L20, 35R30. Keywords: Body force, elastic, ill$-$posed problem, interpolation, Fourier series.