Hartmut Logemann

Conditions for Robustness and Nonrobustness of theStability of Feedback Systems with Respect to Small Delays inthe Feedback Loop

It has been observed that for many stable feedback control systems, the introduction of arbitrarily small time delays into the loop causes instability. In this paper we present a systematic frequency domain treatment of this phenomenon for distributed parameter systems. We consider the class of all matrix-valued transfer functions which are bounded on some right half-plane and which have a limit at

The effect of small delays in the feedback loop on the stability of neutral systems

+\spinfty

Low-Gain Control of Uncertain Regular Linear Systems

along the real axis. Such transfer functions are called regular. Under the assumption that a regular transfer function is stabilized by unity output feedback, we give sufficient conditions for the robustness and for the nonrobustness of the stability with respect to small time delays in the loop. These conditions are given in terms of the high-frequency behavior of the open-loop system. Moreover, we discuss robustness of stability with respect to small delays for feedback systems with dynamic compensators. In particular, we show that if a plant with infinitely many poles in the closed right half-plane is stabilized by a controller, then the stability is not robust with respect to delays. We show that the instability created by small delays is itself robust to small delays. Three examples are given to illustrate these results.

PID control of second-order systems with hysteresis

It is well-known that exponential stabilization of a neutral system with unstable difference operator is only possible by allowing for control laws containing derivative feedback. We show that closed-loop stability of a neutral system with unstable open-loop difference operator obtained by applying a derivative feedback scheme is extremely sensitive to arbitrarily small time delays in the feedback loop.

The Circle Criterion and Input-to-State Stability

It is well known that closing the loop around an exponentially stable, finite-dimensional, linear, time-invariant plant with square transfer-function matrix

Low-Gain Integral Control of Infinite-Dimensional Regular Linear Systems Subject to Input Hysteresis

\BG(s)

Destabilizing effects of small time delays on feedback-controlled descriptor systems ☆

compensated by a controller of the form

Brief Low-gain integral control of continuous-time linear systems subject to input and output nonlinearities

(k/s)\Gamma_0

Integral control of linear systems with actuator nonlinearities: lower bounds for the maximal regulating gain

, where

Adaptive stabilization of infinite-dimensional systems

k\in {\Bbb R}