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

https://www.jstage.jst.go.jp/article/sicetr1965/18/5/18_5_464/_pdf

On Explicit Solutions of the Algebraic Lyapunov Matrix Equation and Bounds for their Extremal Characteristic Roots

Delay-Dependent Stability Condition for Linear Time-Delay Systems

Whether the Hurwitz stability of segment polynomials implies the quadratic stability is an interesting subject in relating to the Lyapunov route to Kharitonov's theorem. Noting that segment polynomial families associated with a strictly positive real function are not only stable, but quadratically stable independently of their length, we have examined if such is possible with nonpositive real functions, taking second-degree polynomials. The answer is that the quadratic stability independent of the length implies and is implied by the positive realness. Based on this fact, we have shown that even second-degree interval polynomials cannot always be quadratically stable.

Takehiro Mori

Papers

On Explicit Solutions of the Algebraic Lyapunov Matrix Equation and Bounds for their Extremal Characteristic Roots

Delay-Dependent Stability Condition for Linear Time-Delay Systems

On quadratic Hurwitz stability of segment polynomials

On a Lower Estimate for the Determinant of the Solution to the Lyapunov Matrix Equation

Cyclohexylenedithio Anellated Bis-Fused TTF Donors and Their Conducting Salts.