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

For Schur polynomials with perturbed coefficients, a lower bound is derived for the radius of the hypersphere in the parameter space, within which the perturbed polynomials retain the Schur property. The result is obtained via the Lyapunov matrix equation and is expressed in terms of the size of the solution lo the equation This enables us to estimate the allowable size of the perturbation simply by solving the equation.

Bound for radius of stability-preserving hypersphere in parameter space for Schur polynomials

Aperiodicity is normally defined as a property such that all the roots are simple and negative real, while interval polynomials are referred to as polynomials with coefficients lying within specified closed intervals on the real axis. Several conditions for aperiodicity, including an exact one, are derived. Comments on these conditions are given in contrast to the work of Soh and Berger, who also considered the problem with a modified definition of aperiodicity.

Aperiodicity conditions for Polynomials With Uncertain Coefficient Parameters

A necessary and sufficient condition is derived for a convex combination of two given polynomials to be a convergent polynomial, i.e. a polynomial having roots all within the unit circle in the complex plane. This can be regarded as a discrete counterpart to the existing result for the continuous case. A simple numerical example is provided to demonstrate the theorem obtained.

Convergence condition for convex combinations of two polynomials

On Lower Bounds for the Solution to the Discrete Lyapunov Matrix Equation

Some additional comments are offered on the stability condition for linear discrete systems in Dabke (1983). It is pointed out that the condition can be naturally extended to cover time-varying systems.

Takehiro Mori

Papers

Bound for radius of stability-preserving hypersphere in parameter space for Schur polynomials

Aperiodicity conditions for Polynomials With Uncertain Coefficient Parameters

Convergence condition for convex combinations of two polynomials

On Lower Bounds for the Solution to the Discrete Lyapunov Matrix Equation

Further comments on ‘A simple criterion for stability of linear discrete systems’