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Dynamic robust stabilization of fractional-order linear systems with nonlinear uncertain parameters: An LMI approach [article]

Pouya Badri, Mahdi Sojoodi, Elyar Zavvari
2021 arXiv   pre-print
This paper considers the problem of robust stability and stabilization for linear fractional-order system with nonlinear uncertain parameters, with fractional order 0<a<2.  ...  Keywords: Fractional-order system, nonlinear uncertain parameters, linear matrix inequality (LMI), robust stabilization, dynamic output feedback.  ...  On the other hand, most of nonlinear fractional-order systems can be linearized in practical applications for stability analysis and control purposes.  ... 
arXiv:1902.01238v2 fatcat:ldz2vmyd5rf7dmwaoc5ar2eeje

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

S. Balochian
2014 Bulletin of the Polish Academy of Sciences: Technical Sciences  
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  ...  Then a sliding sector is designed for each subsystem of the LTI-FO switched system.  ...  In [27] the stabilization of a particular class of nonlinear systems of fractional order differential inclusions in fractional derivative chaos systems using variable structure control is considered.  ... 
doi:10.2478/bpasts-2014-0053 fatcat:mo5bxfrtyba3vbmvxc3zlrea3y

Infinite matrix representations of robust stability conditions for discrete-time systems

Yohei Hosoe, Tomomichi Hagiwara
2011 IEEE Conference on Decision and Control and European Control Conference  
To facilitate such a study, this paper gives the infinite matrix representation counterparts of the robust stability conditions in the separatortype robust stability theorems for these approaches.  ...  Through the derivation and comparison of explicit forms of infinitedimensional separators in these two approaches, it is demonstrated that the infinite matrix representation framework leads to a very comprehensible  ...  This paper is concerned with the separator-type robust stability theorem [5] for robust stability analysis of linear time-invariant (LTI) discrete-time systems.  ... 
doi:10.1109/cdc.2011.6160569 dblp:conf/cdc/HosoeH11 fatcat:eixsvjx65beyhe3j32s56bl3nu

Measurement And Symbolic Analysis Of Implemented Multirate Systems

F. Heinle, H.W. Schuessler
1996 Zenodo  
Publication in the conference proceedings of EUSIPCO, Trieste, Italy, 1996  ...  This paper is based on a matrix description of linear MRS 4] that is well suited for a description of arbitrary MRS and an easy analysis of compound systems.  ...  identical with its PP and modulation matrix of MRS: An LTI system can be represented equivalently 7] as an alias-free p p MRS for a simultaneous processing of p subsequent samples.  ... 
doi:10.5281/zenodo.36399 fatcat:r6puztn7gffk7ac7flxmhtvkzm

Gain-scheduling control of machine tools with varying structural flexibility

W. Symens, H. van Brussel, J. Swevers
2004 CIRP annals  
The high accelerations occurring in present-day machine tools are likely to excite the vibration modes of the machine structure.  ...  This paper discusses the gain-scheduling control approach for an experimental set-up containing a flexible beam of which the stiffness depends on its length.  ...  Acknowledgments The authors would like to thank Carsten Scherer, TU Delft, for providing a draft version of the LPVsynthesis toolbox and Gary Balas and Peter Young for providing a draft version of the  ... 
doi:10.1016/s0007-8506(07)60707-0 fatcat:w4brrj55nbblnmi6gffeb4zr2q

Robust Minimum Gain Lemma

Tamas Baar, Tamas Luspay
2021 2021 60th IEEE Conference on Decision and Control (CDC)  
The computation of the minimum sensitivity of uncertain Linear Time Invariant (LTI) systems is presented in the paper.  ...  The extension of the Minimum Gain Lemma is presented for such interconnections, resulting in a convex optimization problem subject to Linear Matrix Inequality (LMI) constraints.  ...  The research leading to these results is part of the FLIPASED project.  ... 
doi:10.1109/cdc45484.2021.9683413 fatcat:6onaqjhqxjbynereszmfxkecbi

Self-scheduled H-infinity control of missile via linear matrix inequalities

Pierre Apkarian, Jean-Marc Biannic, Pascal Gahinet
1995 Journal of Guidance Control and Dynamics  
CONTROL OF MISSILE 533 \) pct K(6) Fig.1 74.. synthesis structure for LPV systems.  ...  It follows that for a frozen value of the parameter, LPV systems can be analyzed as LTI systems.  ... 
doi:10.2514/3.21419 fatcat:5c5y53idqbcnnns4uuvg3hsapi

Robust stability under mixed time-varying, time-invariant and parametric uncertainty

Fernando Paganini
1996 Automatica  
Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for  ...  Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining  ...  Acknowledgements The author wishes t o thank Raffaello D'Andrea for a stimulating discussion, and Geir Dullerud for helpful suggestions. This work was supported by AFOSR.  ... 
doi:10.1016/0005-1098(96)00089-1 fatcat:nixgdtl4nfadfd7esybud2x7se

Cyclic LTI systems in digital signal processing

P.P. Vaidyanathan, A. Kirac
1999 IEEE Transactions on Signal Processing  
State-space descriptions of cyclic LTI systems are introduced, and the notions of reachability and observability of state equations are revisited.  ...  While circular convolution has been the centerpiece of many algorithms in signal processing for decades, such freedom, especially from the viewpoint of linear system theory, has not been studied in the  ...  STATE-SPACE DESCRIPTIONS FOR CYCLIC LTI SYSTEMS In Section II-A, we considered cyclic difference equations and recursive structures for cyclic transfer functions.  ... 
doi:10.1109/78.740127 fatcat:yuyhhy7xxffgnnmc6cpvf2k7ay

State-Space Interpolation for a Gain-Scheduled Autopilot

Daniel J. Stilwell
2001 Journal of Guidance Control and Dynamics  
For purposes of comparison, we also interpolate the two LTI autopilots by linearly interpolating matrix coefficients over the interval [0,20] and simulate the nonlinear closed-loop system.  ...  (p) - —/, iz li, where A; is composed of the matrix coefficients of the plant and LTI controller A;.  ... 
doi:10.2514/2.4766 fatcat:mw5y7eba45gnjc7nif6zcopxd4

Bifrequency and bispectrum maps: a new look at multirate systems with stochastic inputs

S. Akkarakaran, P.P. Vaidyanathan
2000 IEEE Transactions on Signal Processing  
What is the condition if only the sum of their outputs is required to be WSS? When is the output of an LPTV system (for example a uniform filter-bank) WSS for all WSS inputs?  ...  The purpose of this paper is to provide these answers using analysis based on bifrequency maps and bispectra.  ...  effect of an LTI system on the psd matrix.  ... 
doi:10.1109/78.824668 fatcat:z7hg6nulovdz7mknguz2pnttri

A Survey of Fractional Order Calculus Applications of Multiple-Input, Multiple-Output (MIMO) Process Control

Alexandre Marques de Almeida, Marcelo Kaminski Lenzi, Ervin Kaminski Lenzi
2020 Fractal and Fractional  
Furthermore, control system design approaches based on derivatives and integrals of non-integer order, also known as fractional control or fractional order (FO) control, are frequently used for SISO systems  ...  Therefore, this work discusses the state-of-the-art of fractional control applied to MIMO systems.  ...  Acknowledgments: The authors thank CAPES and CNPQ-Brazilian Agencies, for the finantial support and scholarships. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/fractalfract4020022 fatcat:pnbjgdsdczbdjmyhgnz54ijgdi

Page 1476 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
The extension of the model matching result on LTI systems is not straightforward due to the time-varying structure and properties of linear systems.  ...  We develop a framework which provides sufficient convexity conditions, in the form of linear matrix inequalities, for the analysis of constrained quadratic based optimization schemes.  ... 

Convex Necessary and Sufficient Conditions for Frequency Domain Model (In)Validation Under SLTV Structured Uncertainty

M.C. Mazzaro, M. Sznaier
2004 IEEE Transactions on Automatic Control  
Index Terms-Frequency domain model (in)validation, linear matrix inequalities, structured slowly linear time-varying (SLTV) uncertainty. 1 These conditions are also tight in the case of LTI uncertainty  ...  It is well known that in the case of structured LTI uncertainty the problem is NP hard in the number of uncertainty blocks.  ...  , LTI candidate model and a structured uncertainty , , full square block. 2 The block consists of a nominal model of the actual system , and a description, given by the blocks , , and , of how the uncertainty  ... 
doi:10.1109/tac.2004.835387 fatcat:5aj7km5r4nfjhcf2mkqplp5bou

Robust Stability Analysis of a Linear Time-Periodic Active Helicopter Rotor

J.-B. Maurice, Roberto Farolfi, Florian Saupe, Frank Artur King, Walter Fichter
2012 Journal of Guidance Control and Dynamics  
a we 7 wa baal Ai tun oy _ wp > 3wp > waitin [rad/s] Fig. 9 Robust stability analysis of the LTP lifted system (HTF) considering two harmonic and the LTI averaged system for the uncertainty structure of  ...  In the case of the positive feedback system of Fig. 2, the definition of the structured singular value can be extended to Fig. 2. A-structure for robust stability analysis of lifted system.  ... 
doi:10.2514/1.54232 fatcat:e5je4tkbingb3ptqiaxr7y5vye
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