3 research outputs found
LMI-based robust stability and stabilization analysis of fractional-order interval systems with time-varying delay
This paper investigates the robust stability and stabilization analysis of
interval fractional-order systems with time-varying delay. The stability
problem of such systems is solved first, and then using the proposed results a
stabilization theorem is also included, where sufficient conditions are
obtained for designing a stabilizing controller with a predetermined order,
which can be chosen to be as low as possible. Utilizing efficient lemmas, the
stability and stabilization theorems are proposed in the form of LMIs, which is
more suitable to check due to various existing efficient convex optimization
parsers and solvers. Finally, two numerical examples have shown the
effectiveness of our results.Comment: arXiv admin note: text overlap with arXiv:1807.1082
A novel LMI-based Method for Robust Stabilization of Fractional-order Interval Systems with
This paper deals with the problem of robust dynamic output feedback
stabilization of interval fractional-order linear time invariant (FO-LTI)
systems with the fractional order . In this study, a new
formulation based on the null-space analysis of the system matrices is proposed
using linear matrix inequalities (LMIs). The applied uncertain model is the
most complete model of linear interval systems, in which all of the systems
matrices are interval matrices. A robust dynamic output feedback controller is
designed that asymptotically stabilizes the interval FO-LTI system, where no
limiting constraint is assumed on the state space matrices of the uncertain
system. Eventually, a numerical example with simulations is presented to
demonstrate the effectiveness and correctness of the theoretical results.Comment: arXiv admin note: substantial text overlap with arXiv:1807.10827,
arXiv:1701.0534
Robust Stabilization of Fractional-order Interval Systems via Dynamic Output Feedback: An LMI Approach
This paper addresses the problem of robust dynamic output stabilization of
FO-LTI interval systems with the fractional order 0<{\alpha}<2, in terms of
linear matrix inequalities (LMIs). Our purpose is to design a robust dynamic
output feedback controller that asymptotically stabilizes interval
fractional-order linear time-invariant (FO-LTI) systems. Sufficient conditions
are obtained for designing a stabilizing controller with a predetermined order,
which can be chosen to be as low as possible. The LMI-based procedures of
designing robust stabilizing controllers are preserved in spite of the
complexity of assuming the most complete model of linear controller, with
direct feedthrough parameter. Finally, some numerical examples with simulations
are presented to demonstrate the effectiveness and correctness of the
theoretical results. Keywords: Fractional-order system, interval uncertainty,
linear matrix inequality (LMI), robust stabilization, dynamic output feedback.Comment: arXiv admin note: substantial text overlap with arXiv:1701.0534