Preface, Notations 1.Introduction to Time-Delay Systems I.Frequency-Domain Approach 2.Systems with Commensurate Delays 3.Systems withIncommensurate Delays 4.Robust Stability Analysis II.Time Domain Approach 5.Systems with Single Delay 6.Robust Stability Analysis 7.Systems with Multiple and Distributed Delays III.Input-Output Approach 8.Input-output stability A.Matrix Facts B.LMI and Quadratic Integral Inequalities Bibliography Index

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Stability of Time-Delay Systems

Time-delay systems: an overview of some recent advances and open problems

An integral inequality is derived, and applied to the stability problem of time-delay systems using discretized Lyapunov functional formulation. As the result, a simpler stability criterion is derived.

An integral inequality in the stability problem of time-delay systems

This paper concerns a problem of robust stabilization of uncertain state-delayed systems. A new delay-dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities. An algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties.

Delay-dependent robust stabilization of uncertain state-delayed systems

https://hal.inria.fr/inria-00131031/document

Technical Communique: Robust sampled-data stabilization of linear systems: an input delay approach

Criteria for robust stability and stabilization of uncertain linear systems with state delay

Criteria for Robust Stability of Uncertain Linear Systems with Time-Varying State Delays

Robust Stabilization and H∞ Control of Uncertain Linear Time-Delay Systems

This paper considers the problem of output feedback stabilization of continuous time linear systems with a constant time-delay in the state. We develop a delay-dependent method, which is based on linear matrix inequalities, for designing linear dynamic output feedback controllers which ensure global uniform asymptotic stability for any time-delay not larger than a given bound. We also consider the problem of delay-dependent robust stabilization via output feedback for state-delayed systems with norm-bounded parameter uncertainty. In this situation, the solution is given in terms of a generalized eigenvalue problem. The developed stabilization methods can be implemented numerically very efficiently using existing convex and quasi-convex optimization techniques.

Xi Li

Papers

Criteria for robust stability and stabilization of uncertain linear systems with state delay

Criteria for Robust Stability of Uncertain Linear Systems with Time-Varying State Delays

Robust Stabilization and H∞ Control of Uncertain Linear Time-Delay Systems

Output feedback stabilization of linear time-delay systems