Necessary and Sufficient Condition on Controllability and Reachability of Fractional-Order Linear Switched System

2014 ◽  
Vol 541-542 ◽  
pp. 1319-1326
Author(s):  
Cheng Deng ◽  
Wei Zhu
Keyword(s):  
Analytical Solution ◽  
Hybrid Systems ◽  
Fractional Order ◽  
Switched System ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Order Linear ◽  
Arbitrary Switching ◽  
Necessary And Sufficient ◽  
Important System

Fractional-order linear switched system (FLSS) is an important system of hybrid systems. In this paper, by using the analytical solution of FLSS, the necessary and sufficient condition on controllability and reachability of FLSS is given, respectively. The condition shows that if every subsystem is controllable (reachable), then the whole system is also controllable (reachable) for arbitrary switching rules. And if the whole system is controllable (reachable) for arbitrary switching rules, then every subsystem is controllable (reachable).

scholarly journals Self-equilibrium and super-stability of truncated regular polyhedral tensegrity structures: a unified analytical solution

2012 ◽  
Vol 468 (2147) ◽  
pp. 3323-3347 ◽  
Author(s):  
Li-Yuan Zhang ◽  
Yue Li ◽  
Yan-Ping Cao ◽  
Xi-Qiao Feng ◽  
Huajian Gao
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Biological Systems ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Stable States ◽  
Tensegrity Structures ◽  
Closed Form Analytical Solution ◽  
Necessary And Sufficient

In spite of their great importance and numerous applications in many civil, aerospace and biological systems, our understanding of tensegrity structures is still quite preliminary, fragmented and incomplete. Here we establish a unified closed-form analytical solution for the necessary and sufficient condition that ensures the existence of self-equilibrated and super-stable states for truncated regular polyhedral tensegrity structures, including truncated tetrahedral, cubic, octahedral, dodecahedral and icosahedral tensegrities.

Representation of holomorphic functions by schlömilch’s series

2013 ◽  
Vol 16 (2) ◽  
Author(s):  
Peter Rusev
Keyword(s):  
Bessel Function ◽  
Fractional Order ◽  
Holomorphic Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Zero Index

AbstractA necessary and sufficient condition is given for holomorphic functions to be represented by series of the kind $\sum\limits_{n = 0}^\infty {a_n J_0 (nz),z,a_n \in \mathbb{C},} $ where J 0(z) is the Bessel function of first kind with zero index. To derive the result, we use an Erdélyi-Kober operator of fractional order.

scholarly journals Fractional-order LCL filters: principle, frequency characteristics, and their analysis

2021 ◽  
Author(s):  
Junhua Xu ◽  
Xiaocong Li ◽  
Xueli Luo ◽  
Liliang Hou ◽  
Jianbo Qin ◽  
...  
Keyword(s):  
Fractional Order ◽  
Theoretical Basis ◽  
Digital Simulation ◽  
Frequency Characteristics ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Operating Characteristics ◽  
Theoretical Derivation ◽  
Integer Order ◽  
Necessary And Sufficient

Abstract In this paper, a fractional-order LCL (FOLCL) filter is constructed by introducing fractional-order inductors (FOIs) and fractional-order capacitors (FOCs) to replace the inductors and capacitors in a traditional integer-order LCL (IOLCL) filter, respectively. The principle and frequency characteristics of an FOLCL filter are systematically studied, and five important properties are derived and demonstrated in-depth. One of the most important achievements is that we discover the necessary and sufficient condition for the existence of resonance for an FOLCL filter, that is, the sum of the order of the FOIs and the FOC is equal to 2, which provides a theoretical basis for avoiding the resonance of an FOLCL filter effectively in design. The correctness of the theoretical derivation and analysis are verified by digital simulation. Compared with an IOLCL filter, an FOLCL filter presents more flexible and diverse operating characteristics and has a broader application prospect.

scholarly journals Consensus Analysis of Fractional-Order Multiagent Systems with Double-Integrator

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Chunde Yang ◽  
Wenjing Li ◽  
Wei Zhu
Keyword(s):  
Multiagent Systems ◽  
Fractional Order ◽  
Spanning Tree ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Consensus Analysis ◽  
Directed Spanning Tree ◽  
Necessary And Sufficient ◽  
Theoretical Results ◽  
Double Integrator

In nature, many phenomena can be explained by coordinated behavior of agents with fractional-order dynamics. In this paper, the consensus problem of fractional-order multiagent systems with double-integrator is studied, where the fractional-order satisfies0<α<2. Based on the fractional-order stability theory, Mittag-Leffler function, and Laplace transform, a necessary and sufficient condition is obtained under the assumption that the directed graph for the communication network contains a directed spanning tree. Finally, an example with simulation is presented to illustrate the theoretical results.

scholarly journals Stabilization of autonomous linear time invariant fractional order derivative switched systems with different derivative in subsystems

2014 ◽  
Vol 62 (3) ◽  
pp. 495-503 ◽  
Author(s):  
S. Balochian
Keyword(s):  
Fractional Order ◽  
Linear Time ◽  
Variable Structure ◽  
Switched System ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Linear Time Invariant ◽  
Necessary And Sufficient ◽  
Time Invariant ◽  
Derivative Order

Abstract In this paper, the stabilization problem of a autonomous linear time invariant fractional order (LTI-FO) switched system with different derivative order in subsystems is outlined. First, necessary and sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems based on the convex analysis and linear matrix inequality (LMI) for two subsystems is presented and proved. Also, sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems for more than two subsystems is proved. Then a sliding sector is designed for each subsystem of the LTI-FO switched system. Finally, a switching control law is designed to switch the LTI-FO switched system among subsystems to ensure the decrease of the norm of the switched system. Simulation results are given to show the effectiveness of the proposed variable structure controller.

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