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Qualitative Analysis of Switched Discrete-Time Descriptor Systems
Guisheng Zhai,Joe Imae,Xuping Xu,Tomoaki Kobayashi 제어·로봇·시스템학회 2009 International Journal of Control, Automation, and Vol.7 No.4
In this paper, we consider stability analysis and design for switched systems consisting of linear discrete-time descriptor subsystems. When all descriptor subsystems are stable, we show that if the descriptor matrix and all the subsystem matrices are commutative pairwise, then the switched system is stable under arbitrary switching. We also extend the result to the case where all subsystems have different descriptor matrices. Under the same commutation condition, we show that in the case where none of the descriptor subsystems is stable, if there is a stable combination of the unstable descriptor subsystems, then we establish a class of switching laws which stabilize the switched descriptor system. All the results are natural but important extensions to the existing results for switched systems composed of state space subsystems.
Stability Analysis and Design for Switched Descriptor Systems
Guisheng Zhai,Ryuuen Kou,Joe Imae,Tomoaki Kobayashi 제어·로봇·시스템학회 2009 International Journal of Control, Automation, and Vol.7 No.3
In this paper, we consider stability analysis and design for switched systems consisting of linear descriptor systems that have the same descriptor matrix. When all descriptor systems are stable, we show that if the descriptor matrix and all the system matrices are commutative pairwise, then the switched system is stable under arbitrary switching. This is an extension of the existing well known re-sult in [1] for switched linear systems with state space models to switched descriptor systems. Under the same commutation condition, we also show that in the case where all descriptor systems are not stable, if there is a stable convex combination of the unstable descriptor systems, then we can establish a class of switching laws which stabilize the switched system. We finally make some discussion about obtaining the stable convex combination by solving a matrix inequality efficiently, and about relaxing the commutation condition for stabilizability of the switched system.
Improved Synchronization Analysis for Delayed Lur’e Systems Using Improved Technique
Yefan Wu,Lianglin Xiong,Guisheng Zhai,Tao Wu 제어·로봇·시스템학회 2021 International Journal of Control, Automation, and Vol.19 No.4
The master-slave synchronization (MSS) issue of chaotic Lur’e systems (LSs) with time-varying delay (TVD) is explored in this work by means of feedback control. After taking the nonlinear function into full consideration, a creative Lyapunov-Krasovskii functional (LKF) is attained. Then novel criteria which ensure the synchronization of the studied systems are obtained with the aid of the improved inequality technique and the reciprocally convex combination method to cope with the derivative of LKF. The effectiveness and virtues of the synchronization conditions are testified via the notable Chua’s circuit in three different cases.
An LQ Approach to Constrained Nonlinear Optimal Control Problems via Riccati Transformation
Joe Imae,Tomonari Ando,Tomoaki Kobayashi,Guisheng Zhai 제어로봇시스템학회 2009 제어로봇시스템학회 국제학술대회 논문집 Vol.2009 No.8
A new algorithm for numerical solutions of constrained nonlinear optimal control problems has been proposed based on Riccati transformation. First, we approximate the constrained nonlinear optimal control problems by the Taylor expansion technique. Then, constructing the constrained LQ problems as the accessory problems, we analytically solve them via Riccati transformation. Finally, repeating the above procedure, we eventually obtain the optimal solutions for constrained nonlinear optimal control problems. The effectiveness of the proposed algorithm has been demonstrated through simulation.