Phan Thành Nam

Discrete Wirtinger-based inequality and its application

In this paper, we derive a new inequality, which encompasses the discrete Jensen inequality. The new inequality is applied to analyze stability of linear discrete systems with an interval time-varying delay and a less conservative stability condition is obtained. Two numerical examples are given to show the effectiveness of the obtained stability condition.

Technical communique: Further result on reachable set bounding for linear uncertain polytopic systems with interval time-varying delays

The problem of reachable set estimation of linear uncertain polytopic time-varying delay systems subject to bounded peak inputs is studied in this paper. The delays considered in this paper are assumed to be non-differentiable and vary within an interval where the lower and upper bounds are known. Based on the Lyapunov-Krasovskii method and delay decomposition technique, a sufficient condition for the existence of a ball that bounds the reachable set of the system is proposed in terms of matrix inequalities containing only one scalar which can be solved by using an one-dimensional search method and Matlabs LMI Toolbox and allow us to find the smallest radius. A numerical example is given to illustrate the effectiveness of the proposed result.

Fluctuations around Hartree states in the mean-field regime

We consider the dynamics of a large system of

Partial state estimation for linear systems with output and input time delays

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ε-bounded state estimation for time-delay systems with bounded disturbances

interacting bosons in the mean-field regime where the interaction is of order

Reachable set bounding for nonlinear perturbed time-delay systems: The smallest bound

1/N

Discrete inequalities based on multiple auxiliary functions and their applications to stability analysis of time-delay systems

. We prove that the fluctuations around the nonlinear Hartree state are generated by an effective quadratic Hamiltonian in Fock space, which is derived from Bogoliubovs approximation. We use a direct method in the

Bogoliubov correction to the mean-field dynamics of interacting bosons

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Collective Excitations of Bose Gases in the Mean-Field Regime

-particle space, which is different from the one based on coherent states in Fock space.

Exponential Convergence of Time-Delay Systems in the Presence of Bounded Disturbances

This paper deals with the problem of partial state observer design for linear systems that are subject to time delays in the measured output as well as the control input. By choosing a set of appropriate augmented Lyapunov-Krasovskii functionals with a triple-integral term and using the information of both the delayed output and input, a novel approach to design a minimal-order observer is proposed to guarantee that the observer error is ε-convergent with an exponential rate. Existence conditions of such an observer are derived in terms of matrix inequalities for the cases with time delays in both the output and input and with output delay only. Constructive design algorithms are introduced. Numerical examples are provided to illustrate the design procedure, practicality and effectiveness of the proposed observer.