报告学者：Rachid Malti

报告者单位：Université de Bordeaux

报告时间：2024年7月6日（周六）14:45-15:20

报告地点：红果园三层多功能厅 

报告摘要：This talk presents recent results [1], concerning robust stability analysis of LTI systems having irrational transfer functions which cover a wide variety of linear systems including distributed parameter systems that are solutions of partial differential equations, time-delay rational systems, and fractional order systems. Such systems, described by irrational transfer functions, may be of infinite dimension, typically having an infinite number of poles and/or zeros, rendering their stability analysis more challenging as compared to their finite-dimensional counterparts. First, it is proven that, under mild hypotheses, new poles may appear to the right of a vertical axis of abscissa γ (when γ = 0: imaginary axis) through a continuous variation of parameters only if existing poles to the left of γ cross the vertical axis. Hence, by determining parametric values for which the crossing occurs, known as stability crossing sets (SCS), the entire parametric space is separated into regions within which the number of right-half poles (including multiplicities) is invariant. Based on the aforementioned result, a robust estimation algorithm of the SCS is formulated as an interval constraint satisfaction problem and solved using guaranteed methods from interval arithmetics. The developed algorithm is applied for assessing stability of (i) a controlled parabolic 1D partial differential equation, namely the heat equation, in finite and semi-infinite media, (ii) time-delay rational systems with distributed and retarded type delays, (iii) fractional systems, providing stability results even for incommensurate differentiation orders. 

简介：Rachid Malti is holding a position of full professor in Automatic Control and Computer Engineering at the Université de Bordeaux, France. His main research interests include fractional differentiation and its applications in automatic control and system identification. He is currently working in several application areas such as modeling of Lithium-ion batteries and decision planning in autonomous vehicles. He is developing, with his colleagues, the object oriented CRONE toolbox for fractional systems, freely available. He is co-chair of the steering committee, co-chair of the International Program Committee (IPC) and co-organizer of the ICFDA conference, 10th-12th July 2024,  Bordeaux. He is also a member of two IFAC technical committees, namely 1.1 "Modelling, Identification and Signal Processing" and 2.2 "Linear Control Systems".