scholarly journals Upper Bounds for the Distance between a Controllable Switched Linear System and the Set of Uncontrollable Ones

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Josep Clotet ◽  
M. Dolors Magret
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Upper Bound ◽  
Natural Generalization ◽  
Upper Bounds ◽  
Controllable System ◽  
Switched Linear System ◽  
Switched Linear Systems ◽  
The Real ◽  
Dense Set

The set of controllable switched linear systems is an open and dense set in the space of all switched linear systems. Therefore it makes sense to compute the distance from a controllable system to the nearest uncontrollable one. In the case of a standard system,x˙t=Axt+But, R. Eising, D. Boley, and W. S. Lu obtain some results for this distance, both in the complex and real cases. In this work we explore this distance, for switched linear systems in the real case, obtaining upper bounds for it. The main contribution of the paper is to prove that a natural generalization of the upper bound obtained by D. Boley and W. S. Lu is true in the case of switched linear systems.

scholarly journals Inversion-Based Approach for Detection and Isolation of Faults in Switched Linear Systems

Electronics ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 561 ◽  
Author(s):  
Alexandre Miguel Silveira ◽  
Rui Esteves Araújo
Keyword(s):  
Linear Systems ◽  
Low Cost ◽  
Inverse Model ◽  
Fault Detection And Isolation ◽  
Switched Linear System ◽  
Switched Linear Systems ◽  
Switching Sequence ◽  
System A ◽  
Unknown Disturbances ◽  
Abrupt Faults

This paper addresses the problem of the left inversion of switched linear systems from a diagnostics perspective. The problem of left inversion is to reconstruct the input of a system with the knowledge of its output, whose differentiation is usually required. In the case of this work, the objective is to reconstruct the system’s unknown inputs, based on the knowledge of its outputs, switching sequence and known inputs. With the inverse model of the switched linear system, a real-time Fault Detection and Isolation (FDI) algorithm with an integrated Fuzzy Logic System (FLS) that is capable of detecting and isolating abrupt faults occurring in the system is developed. In order to attenuate the effects of unknown disturbances and noise at the output of the inverse model, a smoothing strategy is also used. The results are illustrated with an example. The performance of the method is validated experimentally in a dc-dc boost converter, using a low-cost microcontroller, without any additional components.

Parameterized Regulator Design Method for Switched Linear Systems

2006 ◽  
Author(s):  
Zhizheng Wu ◽  
Foued Ben Amara
Keyword(s):  
Linear Systems ◽  
Closed Loop ◽  
Design Method ◽  
Loop System ◽  
Closed Loop System ◽  
Switched Linear System ◽  
Switched Linear Systems ◽  
Central Controller ◽  
Synthesis Approach ◽  
System Switching

In this paper, a parameterized regulator design method based on bilinear matrix inequalities (BMIs) is presented for switched linear systems, where it is desired to reject known disturbance signals and/or track known reference inputs. Switching among plant models as well among disturbance and reference signals is defined according to a switching surface. The regulator design approach consists of three steps. The first step consists of constructing a switched observer-based state-feedback central controller for the switched linear system. Switching in the controller is performed according to the same switching rule as in the plant. The second step involves augmenting the switched central-controller to construct a parameterized set of switched controllers. Conditions for internal stability of the resulting switched closed loop system are presented. In the third step, regulation conditions are derived for the switched closed loop system. Based on the regulation conditions, a regulator synthesis approach is proposed based on solving properly formulated BMIs. Finally, a numerical example is presented to illustrate the performance of the proposed regulator.

Continuous-time Identification for a class of Switched Linear Systems

2020 ◽  
Author(s):  
Abdelhak Goudjil ◽  
Mathieu Pouliquen ◽  
Eric Pigeon ◽  
Olivier Gehan ◽  
Tristan Bonargent
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Switched Linear Systems

scholarly journals A Viable Approach to Mitigating Irreproducibility

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 205-215
Author(s):  
David Trafimow ◽  
Tonghui Wang ◽  
Cong Wang
Keyword(s):  
Upper Bound ◽  
Recent Article ◽  
Practical Problem ◽  
The Real ◽  
Viable Approach ◽  
Real Universe ◽  
The Ideal

In a recent article, Trafimow suggested the usefulness of imagining an ideal universe where the only difference between original and replication experiments is the operation of randomness. This contrasts with replication in the real universe where systematicity, as well as randomness, creates differences between original and replication experiments. Although Trafimow showed (a) that the probability of replication in the ideal universe places an upper bound on the probability of replication in the real universe, and (b) how to calculate the probability of replication in the ideal universe, the conception is afflicted with an important practical problem. Too many participants are needed to render the approach palatable to most researchers. The present aim is to address this problem. Embracing skewness is an important part of the solution.

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