Finite settling time stabilisation: the robust SISO case

This article deals with the problem of robustness to multiplicative plant perturbations for the case of finite settling time stabilisation (FSTS) of single input single output (SISO), linear, discrete-time systems. FSTS is a generalisation of the deadbeat control and as in the case of deadbeat control the main feature of FSTS is the placement of all closed-loop poles at the origin of the z-plane. This makes FSTS sensitive to plant perturbations hence, the need of robust design. An efficient robustness index is introduced and the problem is reduced to a finite linear programme where all the benefits of the simplex method, such as effectiveness, efficiency and ability to provide complete solution to the optimisation problem, can be exploited

The pseudo McMillan degree of implicit transfer functions of RLC networks

We study the structure of a given RLC network without sources. Since the McMillan degree of the implicit transfer function is not a suitable measure of complexity of the network, we introduce the pseudo McMillan degree to overcome these shortcomings.Using modified nodal analysis models, which are linked directly to the natural network topology, we shaw that the pseudo-McMillan degree equals the sum of the number of capacitors and inductors minus the number of fundamental loops of capacitors and fundamental cutsets of inductors; this is the number of independent dynamic elements in the network. Exploiting this representation we derive a minimal realization of the given RLC network, that is one where the number of independent differential equations equals the pseudo McMillan degree

Constrained pre-equalization accounting for multi-path fading emulated using large RC networks: applications to wireless and photonics communications

Multi-path propagation is modelled assuming a multi-layer RC network with randomly allocated resistors and capacitors to represent the transmission medium. Due to frequency-selective attenuation, the waveforms associated with each propagation path incur path-dependent distortion. A pre-equalization procedure that takes into account the capabilities of the transmission source as well as the transmission properties of the medium is developed. The problem is cast within a Mixed Integer Linear Programming optimization framework that uses the developed nominal RC network model, with the excitation waveform customized to optimize signal fidelity from the transmitter to the receiver. The objective is to match a Gaussian pulse input accounting for frequency regions where there would be pronounced fading. Simulations are carried out with different network realizations in order to evaluate the sensitivity of the solution with respect to changes in the transmission medium mimicking the multi-path propagation. The proposed approach is of relevance where equalization techniques are difficult to implement. Applications are discussed within the context of emergent communication modalities across the EM spectrum such as light percolation as well as emergent indoor communications assuming various modulation protocols or UWB schemes as well as within the context of space division multiplexing

Regulated state synchronization of homogeneous multiagent systems with partial‐state coupling via low‐gain adaptive protocol

This paper studies regulated state synchronization for continuous‐time homogeneous multiagent systems with weakly unstable agents where the reference trajectory is given by a so‐called exosystem. The agents share part of their state over a communication network. We assume that the communication topology is completely unknown and directed. An algebraic Riccati equation–based low‐gain adaptive nonlinear dynamic protocol design is presented to achieve the regulated state synchronizations. Utilizing the adaptive control, our nonlinear dynamic protocol is universal and does not depend on any information about the communication topology or the number of agents