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

By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. The article surveys developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching sequences, and construction of stabilizing switching sequences. We also provide motivation for studying these problems by discussing how they arise in connection with various questions of interest in control theory and applications.

Basic problems in stability and design of switched systems

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

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

This technical note studies a resilient control problem for discrete-time, linear time-invariant systems subject to state and input constraints. State measurements and control commands are transmitted over a communication network and could be corrupted by adversaries. In particular, we consider the replay attackers who maliciously repeat the messages sent from the operator to the actuator. We propose a variation of the receding-horizon control law to deal with the replay attacks and analyze the resulting system performance degradation. A class of competitive (resp. cooperative) resource allocation problems for resilient networked control systems is also investigated.

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On the Performance Analysis of Resilient Networked Control Systems Under Replay Attacks

On the Condition for the Eigenvalues of a Matrix to be Distributed in a Sector

On Interval Stability for Feedback Systems with Time-Delay

On Stability of a Class of Linear Differential Difference Systems

It is known that the discrete Lyapunov matrix equation has a positive semidefinite symmetric solution under an appropriate condition. This note proves the fact that the number of positive eigenvalues of the solution is equal to the rank of the controllability matrix formed from the coefficient matrices.

Number of positive eigenvalues of the solution to the discrete Lyapunov matrix equation

The present paper extends Tsypkin and Polyak's theorem (1991) to a family of polynomials that represents a special class of affine perturbations. The intuitive meaning of their theorem is clarified from the point of view of stability robustness. A similar extension for the discrete-time case is also provided. >

Takehiro Mori

Papers

On the Condition for the Eigenvalues of a Matrix to be Distributed in a Sector

On Interval Stability for Feedback Systems with Time-Delay

On Stability of a Class of Linear Differential Difference Systems

Number of positive eigenvalues of the solution to the discrete Lyapunov matrix equation

A criterion for l/sup /spl lambda//-robust stability in parameter space