Stability Preserving Transition From Derivative Feedback to Its Difference Counterparts

A class of neutral-type delay differential equations that are effectively retarded

“…Thus, state estimation, which is needed for feedback controller design, requires the designer in one way or other to obtain derivatives of system outputs. For systems that are subject to time delays in observation, as well as ones where model-based observer design is impracticable and instead signal-based methods are needed (e.g., adaptive or decentralized systems), direct computation/approximation of output derivatives for feedback control may be a promising strategy [4], [5], [10]. One natural means for using output derivatives in feedback is through delayed measurement or delayed computation 1 .…”

“…When an open-loop system is not ANCBC, only local results can be obtained. Naturally, for the problem of local stabilization, estimation and enlargement of the resulting domain of attraction has been a topic of intensive study (see, [4], [5], [9], [10], [13], [14] and the references therein).…”

σ‐Stabilization of a Flexible Joint Robotic Arm via Delayed Controllers

“…Even when in the recent decades there is a great development in the control theory, where many sophisticated control schemes have been developed, PID controllers remain as one of the most used control strategies in the industrial environment. According to [11,12], approximately 90-95% of the industrial control loops still use PID-type controllers, many of which do not include the derivative term, mainly because this term induces a noise amplifying e ect that can a ect the system performance [12][13][14] or because the derivative of the state is not available for measurement. Some common strategies to avoid the use of the derivative term and, consequently, the noise amplication problem, are the use of lters, and observers or the implementation of estimation schemes.…”

“…and for an appropriate selection of the delay τ, the closedloop stability is guaranteed [3,[14][15][16]. In this framework, in [17], a method for the migration of a double imaginary characteristic root to the left half-plane or the right halfplane under the variation of two parameters of a quasipolynomial is presented.…”

Dynamic Controllers Which Use Difference Approximates of Output Derivatives and Their Practical Stability

“…For this case, the resulting closed-loop system involves a time-delay originated from taking the difference, and sometimes loses the stability however accurate the approximation is. (e.g., Kokame and Mori 2002).…”