A note on ℒpℒp-norms of fractional systems

This paper discusses @?"p-norm (1@?p@?~) finiteness property of the impulse response of a stable fractional system cascaded with a pure fractional integrator. The established results are used to choose a performance index for evaluating the output feedback control system performances.

[1]  I. Podlubny Fractional differential equations , 1998 .

[2]  Mohammad Saleh Tavazoei,et al.  Notes on integral performance indices in fractional-order control systems , 2010 .

[3]  Alain Oustaloup,et al.  Synthesis of fractional Laguerre basis for system approximation , 2007, Autom..

[4]  A. Oustaloup,et al.  Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes , 2004, First International Symposium on Control, Communications and Signal Processing, 2004..

[5]  T. Hartley,et al.  OPTIMAL FRACTIONAL-ORDER DAMPING , 2003 .

[6]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[7]  Samir Ladaci,et al.  Lp-stability analysis of a class of nonlinear fractional differential equations , 2007 .

[8]  A. Oustaloup,et al.  Numerical Simulations of Fractional Systems: An Overview of Existing Methods and Improvements , 2004 .

[9]  Alain Oustaloup,et al.  Object-oriented CRONE toolbox for fractional differential signal processing , 2012, Signal Image Video Process..

[10]  Patrick Lanusse,et al.  CRONE control system design toolbox for the control engineering community: tutorial and case study , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[11]  Y. Chen,et al.  Sub-Optimum H2 Rational Approximations to Fractional Order Linear Systems , 2005 .

[12]  J. Partington,et al.  Coprime factorizations and stability of fractional differential systems , 2000 .

[13]  Alain Oustaloup,et al.  Analytical computation of the H2-norm of fractional commensurate transfer functions , 2011, Autom..

[14]  Xavier Moreau,et al.  Stability and resonance conditions of elementary fractional transfer functions , 2011, Autom..

[15]  Patrick Lanusse,et al.  CRONE Control-System Design Toolbox for the Control Engineering Community , 2013 .

[16]  D. Matignon Stability properties for generalized fractional differential systems , 1998 .

[17]  Hüseyin Akçay,et al.  Synthesis of Complete Orthonormal Fractional Basis Functions With Prescribed Poles , 2008, IEEE Transactions on Signal Processing.

[18]  Mathieu Moze,et al.  LMI stability conditions for fractional order systems , 2010, Comput. Math. Appl..