Stabilizing region of PDμ controller for fractional order system with general interval uncertainties and an interval delay

This paper concentrates on computing the stabilizing region of PD^μ controller for fractional order system with general interval uncertainties and an interval delay. The stabilizing region means the complete/approximate set of PD^μ controllers that stabilize the given closed-loop control system. General interval uncertainties refer to both coefficients and orders of the fractional system suffer from interval uncertainties. Interval delay indicates that the delay also vary in a specified interval.Firstly, a method is presented to calculate the stabilizing region for general interval fractional system with an interval time-constant delay. Based on a novel mapping function and the concept of critical controller parameters, the stabilizing region can be determined numerically. Secondly, the stabilizing region computation problem for general interval fractional system with an interval time-varyingdelay is considered. By applying a revised small-gain theorem, the stabilizing region can be calculated like the time-constant delay case. Thirdly, two alternative methods are proposed to improve the computational efficiency of stabilizing region calculation. Both methods can reduce the number of polynomials which are used to determine the stabilizing region. Examples are followed to illustrate the proposed results.     

Probabilistic-constrained control of interval type-2 T–S fuzzy systems under the multi-node round-robin scheduling protocol

This work concentrates on the control design of interval type-2 (IT2) T–S fuzzy systems under probabilistic saturation constraints. The actual control signals are allowed to exceed some preset thresholds with a certain frequency. Meanwhile, the sensors are governed by the multi-node round-robin scheduling protocol, which permits more than one sensors to transmit their information at every moment. The main objective is to synthesize a fuzzy controller such that the closed-loop system is locally stochastically stable under probabilistic saturated constraints and the multi-node round-robin scheduling protocol. To this end, the probabilistic saturation constraints are characterized by a Bernoulli-distributed stochastic process, and the received state at the controller side is formulated based on an updating rule and a compensation strategy. By constructing new membership functions, a token-dependent control law is subsequently designed. The stability analysis is facilitated by a modified sector condition dealing with the saturation nonlinearities. With suitable selection of initial states, sufficient conditions are derived to achieve the local stochastic stability of the closed-loop IT2 T–S fuzzy system. A larger domain of stochastic stability can be obtained via a searching algorithm. Finally, the proposed method is illustrated via a simulation example.     

Sampled-data H∞ filtering of Takagi–Sugeno fuzzy systems with interval time-varying delays

The sampled-data _H∞$H_{\infty }$ filtering for a continuous-time Takagi–Sugeno fuzzy system with an interval time-varying state delay is investigated, where the measurement outputs from the plant to the filter are assumed to be sampled at discrete instants with a variable period. Firstly, by means of a newly proposed inequality bounding technique and a new Lyapunov–Krasovskii functional, the fuzzy sampled-data _H∞$H_{\infty }$ filtering performance analysis is carried out such that the resultant filter error system is asymptotically stable with a prescribed _H∞$H_{\infty }$ attenuation performance index. Secondly, sufficient conditions on the existence of fuzzy sampled-data _H∞$H_{\infty }$ filters are derived in the simultaneous presence of the time-varying state delay and the variable sampling period. The proposed bounding inequality lies in its more tightness and alleviates the enlargement of some inverse “coefficients” resulting from the utilization of the well-known Jensen integral inequality  . Compared with some existing Lyapunov–Krasovskii functionals, more information about the relationship among the current state and its delayed state is considered. The upper bound of the derivative of the time-varying state delay is not required to be less than one. Different from some existing results in the literature, by applying the proposed results, each different value of such an upper bound (greater than one) leads to a different _H∞$H_{\infty }$ disturbance attenuation level. Finally, a numerical example and a modified continuous stirred tank reactor system are given to show the effectiveness of the proposed results.     

Academy of Opto-Electronics,CAS

The Academy of Opto-Electronics (AOE) is an institution under the direct jurisdiction of the CAS headquarters. Organizationally, it has six components: the head office, the Changchun Institute of Optics, Fine Mechanics & Physics (CIOMP), the Shanghai Institute of Technical Physics (SITP), the Xi’an Institute of Optics & Precision Mechanics (XIOM), the Shanghai Institute of Optics & Fine Me- chanics (SIOM) and the Institute of Optics & Electron- ics (IOE) in Chengdu. The p…     

Robust stability and stabilization of fractional order interval systems with coupling relationships: The 0<α<1 case

In this paper we consider a class of fractional order linear time invariant (FO-LTI) interval systems with linear coupling relationships among the fractional order, the system matrix and the input matrix. We present the sufficient conditions for the robust stability and stabilization of such coupling FO-LTI interval systems with the fractional order α satisfying 0<α<1. All the results are proposed in terms of linear matrix inequalities (LMI). Two numerical examples show that our results are effective for checking the robust asymptotical stability and designing the stabilizing controller for FO-LTI interval systems.     

Mario Bunge (1919–2020): Physicist,philosopher, champion of science,and citizen of the world

Mario Bunge, the centenarian Argentine/Canadian physicist/philosopher passed away in the loving company of his wife Marta and children Eric and Silvia on February 24, 2020 in Montréal, Ontario. This memoriam reviews his life and work, particularly his contributions to physics and philosophy of science.