A fast algorithm to computer the H∞ -norm of a transfer function matrix
Systems & Control Letters
An introduction to infinite-dimensional linear systems theory
An introduction to infinite-dimensional linear systems theory
Robust and optimal control
H∞ -state-feedback control of linear systems with small state de
Systems & Control Letters
Sensitivity to Infinitesimal Delays in Neutral Equations
SIAM Journal on Control and Optimization
Pseudospectral Differencing Methods for Characteristic Roots of Delay Differential Equations
SIAM Journal on Scientific Computing
Stability and Stabilization of Time-Delay Systems (Advances in Design & Control) (Advances in Design and Control)
Applied Numerical Mathematics
Strong Stability of Neutral Equations with an Arbitrary Delay Dependency Structure
SIAM Journal on Control and Optimization
Automatica (Journal of IFAC)
Characterization and Computation of $\mathcal{H}_{\infty}$ Norms for Time-Delay Systems
SIAM Journal on Matrix Analysis and Applications
An eigenvalue based approach for the stabilization of linear time-delay systems of neutral type
Automatica (Journal of IFAC)
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We analyze and design H-infinity controllers for general time-delay systems with time-delays in systems' state, inputs, and outputs. We allow the designer to choose the order of the controller and to introduce constant time-delays into the controller. The closed-loop system of the plant and the controller is modeled by a system of delay differential algebraic equations (DDAEs). The advantage of the DDAE modeling framework is that any interconnection of systems and controllers prone to various types of delays can be dealt with in a systematic way, without using any elimination technique. We present a predictor-corrector algorithm for the H-infinity norm computation of systems described by DDAEs. Instrumental to this we analyze the properties of the H-infinity norm. In particular, we illustrate that it may be sensitive with respect to arbitrarily small delay perturbations. Due to this sensitivity, we introduce the strong H-infinity norm, which explicitly takes into account small delay perturbations, inevitable in any practical control application. We present a numerical algorithm to compute the strong H-infinity norm for DDAEs. Using this algorithm and the computation of the gradient of the strong H-infinity norm with respect to the controller parameters, we minimize the strong H-infinity norm of the closed-loop system based on nonsmooth, nonconvex optimization methods. By this approach, we tune the controller parameters and design H-infinity controllers with a prescribed order or structure.