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Stabilization of fractional order systems using a finite number of state feedback laws

Balochian, S ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1007/s11071-010-9916-y
  3. Abstract:
  4. In this paper, the stabilization of linear time-invariant systems with fractional derivatives using a limited number of available state feedback gains, none of which is individually capable of system stabilization, is studied. In order to solve this problem in fractional order systems, the linear matrix inequality (LMI) approach has been used for fractional order systems. A shadow integer order system for each fractional order system is defined, which has a behavior similar to the fractional order system only from the stabilization point of view. This facilitates the use of Lyapunov function and convex analysis in systems with fractional order 1
  5. Keywords:
  6. Fractional order hybrid system ; Linear matrix inequality (LMI) ; Variable structure control ; Control gains ; Convex analysis ; Finite number ; Fractional derivatives ; Fractional order ; Fractional-order systems ; Integer order ; Linear matrix inequality approach ; Linear time invariant systems ; LMI approach ; Sliding sector ; State feedback gain ; Sufficient conditions ; System stabilization ; Variable structures ; Algebra ; Hybrid systems ; Invariance ; Linear matrix inequalities ; Lyapunov functions ; Stabilization ; Time varying control systems ; State feedback
  7. Source: Nonlinear Dynamics ; Volume 66, Issue 1-2 , 2011 , Pages 141-152 ; 0924090X (ISSN)
  8. URL: http://link.springer.com/article/10.1007%2Fs11071-010-9916-y