ROBUST CONTROLLABILITY OF INTERVAL FRACTIONAL ORDER LINEAR TIME INVARIANT SYSTEMS

We consider uncertain fractional-order linear time invariant (FO-LTI) systems with interval coefficients. Our focus is on the robust controllability issue for interval FO-LTI systems in statespace form. We re-visited the controllability problem for the case when there is no interval uncertainty. It turns out that the stability check for FO-LTI systems amounts to checking the conventional integer order state space using the same state matrix A and the input coupling matrix B. Based on this fact, we further show that, for interval FO-LTI systems, the key is to check the linear dependency of a set of interval vectors. Illustrative examples are presented. Keywords: fractional order systems, robust controllability, interval linear time invariant systems, interval matrix, linear dependency of interval vectors. Introduction Based on fractional order calculu

System Simulation Techniques with MATLAB and Simulink

System Simulation Techniques with MATLAB and Simulink comprehensively explains how to use MATLAB and Simulink to perform dynamic systems simulation tasks for engineering and non-engineering applications. This book begins with covering the fundamentals of MATLAB programming and applications, and the solutions to different mathematical problems in simulation. The fundamentals of Simulink modelling and simulation are then presented, followed by coverage of intermediate level modelling skills and more advanced techniques in Simulink modelling and applications. Finally the modelling and simulation of engineering and non-engineering systems are presented. The areas covered include electrical, electronic systems, mechanical systems, pharmacokinetic systems, video and image processing systems and discrete event systems. Hardware-in-the-loop simulation and real-time application are also discussed. Key features: Progressive building of simulation skills using Simulink, from basics through to advanced levels, with illustrations and examples Wide coverage of simulation topics of applications from engineering to non-engineering systems Dedicated chapter on hardware-in-the-loop simulation and real time control End of chapter exercises A companion website hosting a solution manual and powerpoint slides System Simulation Techniques with MATLAB and Simulink is a suitable textbook for senior undergraduate/postgraduate courses covering modelling and simulation, and is also an ideal reference for researchers and practitioners in industry

超薄四面体非晶碳膜光学常数的精确测定

Objective To explore accurate measurement of optical constants of the ultrathin tetrahedral amorphous carbon (ta-C) films by combined usage of spectral ellipsometry (SE) and spectrophotometry. Methods As the amount of unknown parameters determined by ellipsometry method was larger than the number of equations and the ellipsometric equations had no unique solution, the accurate determination of the optical constants of the ultrathin ta-C film accurately was difficult when independently using ellipsometric parameters for fitting due to the strong statistical influence of the film thickness on refractive index and extinction coefficient. Therefore, in this paper, ellipsometric parameters and transmittance (hereinafter referred to as SE+T) were simultaneously fitted to obtain optical constants more easily and rapidly. Results The results showed that the film had typical characteristics of amorphous carbon films. There were obvious differences in optical constants obtained by SE and SE+T. The maximum difference value of extinction coefficient k was up to 0.020 in the visible and infrared area and was 0.005 in the ultraviolet area. The maximum difference value of the refractive index n was 0.04 at wavelengths above 500 nm. The n value tended to be consistent by the two methods in the ultraviolet and visible area. The fitting results had better uniqueness by SE+T and the fitted optical constants were smooth. Conclusion This method of SE+T is suitable for accurate measurement of optical constants of ultrathin ta-C films within measurement range