This paper investigates the $H_{\infty }$ state estimation problem for a class of discrete-time nonlinear singularly perturbed complex networks (SPCNs) under the Round-Robin (RR) protocol. A discrete-time nonlinear SPCN model is first devised on two time scales with their discrepancies reflected by a singular perturbation parameter (SPP). The network measurement outputs are transmitted via a communication network where the data transmissions are scheduled by the RR protocol with hope to avoid the undesired data collision. The error dynamics of the state estimation is governed by a switched system with a periodic switching parameter. A novel Lyapunov function is constructed that is dependent on both the transmission order and the SPP. By establishing a key lemma specifically tackling the SPP, sufficient conditions are obtained such that, for any SPP less than or equal to a predefined upper bound, the error dynamics of the state estimation is asymptotically stable and satisfies a prescribed $H_{\infty }$ performance requirement. Furthermore, the explicit parameterization of the desired state estimator is given by means of the solution to a set of matrix inequalities, and the upper bound of the SPP is then evaluated in the feasibility of these matrix inequalities. Moreover, the corresponding results for linear discrete-time SPCNs are derived as corollaries. A numerical example is given to illustrate the effectiveness of the proposed state estimator design scheme.

$H_{\infty}$ State Estimation for Discrete-Time Nonlinear Singularly Perturbed Complex Networks Under the Round-Robin Protocol

The accumulation of dust particles on the surface of photovoltaic (PV) panel greatly affects its performance especially in the dusty areas. In the present work, an experimental and theoretical study has been carried out to investigate the effect of sand dust concentration on the efficiency of PV panels. A stand-alone PV system is designed to carry out this work. The I–V characteristics have been measured simultaneously for both clean and dusty modules. It has been found that the short circuit current and the maximum output power decrease significantly as dust particles start to accumulate on the panel surface up to a concentration of 1 g/m2, but the rate of decrease is slower for concentrations beyond that value. The reduction in short circuit current in one sample of study is found to be ∼40%, whereas it is ∼34% in the maximum output power. In contrast, it is stated that the open circuit voltage is not sensitive to sand dust accumulation. A significant degradation in the efficiency of PV modules is obser...

A new correlation between photovoltaic panel's efficiency and amount of sand dust accumulated on their surface

This paper presents an overview of recent developments in the theory of singular perturbations and time scales (SPaTS) in discrete control systems. The focus is in three directions: modeling, analysis, and control. First, sources of discrete models and the effect of the discretizing interval on the modeling are reviewed. Then the analysis of two-time scale systems is presented to bring out typical characteristic features of SPaTS. Finally, in the control of the two-time scale systems, the important issue of multirate sampling is addressed. The bibliography containing over 100 titles is included.

Singular perturbations and time scales (SPaTS) in discrete control systems-an overview

The paper presents the review of various types of discrete singularly perturbed control problems and methods for solving them. The bibliography containing 157 titles is included.

Discrete singularly perturbed control problems (A survey)

A two-stage observer-based controller design of discrete two-time-scale (DTTS) systems is presented in this paper. The necessary and sufficient conditions for this kind of controlled system are all addressed. The robust slow-observer-based (SOB) controller is investigated in detail. For a fast sampling rate model, prediction type observer-based controller and SOB controller are proposed. Both prediction type and current estimation type observer-based controller and SOB controllers are developed for a slow sampling rate model of DTTS systems. A twin-engine aviation aircraft is utilized to illustrate the derived schemes.

On the composite and reduced observer-based control of discrete two-time-scale systems

The design of state observers and stabilising controllers for singularly perturbed discrete systems is studied in the paper. Noting the duality between the observer problem and the eigenvalue assignment problem, full-order observers are constructed by a systematic approach, which is based on time-scale decomposition concepts. By applying these results, stabilising problems for singularly perturbed discrete systems with inaccessible states are investigated. Finally, an application to a ninth-order boiler model is discussed.

H. Kando

Papers

Design of observers and stabilising feedback controllers for singularly perturbed discrete systems