Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

In this paper, the state estimation problem is investigated for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays. The norm-bounded uncertainties enter into the system in a randomly way, and such randomly occurring uncertainties (ROUs) obey certain Bernoulli distributed white noise sequence with known conditional probability. By constructing a new Lyapunov–Krasovskii functional, sufficient conditions are proposed to guarantee the convergence of the estimation error for all discrete time-varying delays, ROUs and distributed sensor delays. Subsequently, the explicit form of the estimator parameter is derived by solving two linear matrix inequalities (LMIs) which can be easily tested by using standard numerical software. Finally, a simulation example is given to illustrate the feasibility and effectiveness of the proposed estimation scheme.

State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays

H∞H∞ consensus control for multi-agent systems with missing measurements: The finite-horizon case ☆

Copyright © 2013 Jun Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

/pdf/recent-advances-on-recursive-filtering-and-sliding-mode-2k1qsie5sd.pdf

Recent Advances on Recursive Filtering and Sliding Mode Design for Networked Nonlinear Stochastic Systems: A Survey

Copyright © 2014 Yamin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

/pdf/robust-e-control-for-a-class-of-discrete-time-delay-cbrtdfoozo.pdf

Robust Η∞Control for a Class of Discrete Time-Delay Stochastic Systems with Randomly Occurring Nonlinearities

In this work, delay-dependent stability conditions for systems described by delayed differential equations are presented. The employment of a special transformation to a state space representation named Benrejeb characteristic arrow matrix permits to determine new asymptotic stability conditions. Illustrative examples are presented to show the effectiveness of the proposed approach.

https://www.tandfonline.com/doi/pdf/10.1080/21642583.2013.775537

New delay-dependent stability conditions for linear systems with delay

In this paper, new practical stability conditions for a class of nonlinear time varying delay systems are proposed. The study is based on the use of a specific state space description, known as the Benrejeb characteristic arrow form matrix, and aggregation techniques to obtain delay-dependent stability conditions. Application of this method to delayed Lurie–Postnikov nonlinear systems is given. Illustrative examples are presented to show the effectiveness of the proposed approach.

New stability conditions for nonlinear time varying delay systems

In this paper a new practical stability conditions for delayed Lur'e Postnikov system are proposed. The study use a specific form state space description, named, Benrejeb characteristic arrow matrix. An illustrative example is presented to show the efficiency of proposed method.

New stability conditions for nonlinear time delay systems

In this paper, the stabilizing regions of a first-order controller for an all pole system with time delay are determined via parametric methods. First, a necessary condition is used to determine the admissible ranges of one of the controllerpsilas parameters. Then, for a fixed value of this parameter the stabilizing regions in the remaining two parameters are determined using the D-decomposition method. The approach used can be applied to determine stabilizing regions of a PID controller. Finally, examples are given to illustrate the proposed approach.

Stabilizing first-order controllers for n-th order all pole plants with time delay

We consider stabilizing first-order
systems with time delay. The set of all stabilizing proportional-integral
PI controllers are determined using an extension of the
Hermite-Biehler theorem. The time delay is approximated by a
second-order Pade approximation. For uncertain plants, with
interval type uncertainty, robust stabilizing PI controllers are
determined.

/pdf/pi-controller-design-for-time-delay-systems-using-an-2c7y1lw6q2.pdf

Sami Elmadssia

Papers

New delay-dependent stability conditions for linear systems with delay

New stability conditions for nonlinear time varying delay systems

New stability conditions for nonlinear time delay systems

Stabilizing first-order controllers for n-th order all pole plants with time delay

PI Controller Design for Time Delay Systems Using an Extension of the Hermite-Biehler Theorem