Asymptotics of the Principal Eigenvalue for a Linear Time-Periodic Parabolic Operator I: Large Advection

AbstractThis paper characterizes whether or not\Sigma_{\infty}\equiv\lim_{\lambda\uparrow\infty}\sigma[\mathcal{P}+\lambda m(% x,t),\mathfrak{B},Q_{T}]is finite, where {m\gneq 0} is T-periodic and {\sigma[\mathcal{P}+\lambda m(x,t),\mathfrak{B},Q_{T}]} stands for the principal eigenvalue of the parabolic operator {\mathcal{P}+\lambda m(x,t)} in {Q_{T}\equiv\Omega\times[0,T]} subject to a general boundary operator of mixed type, {\mathfrak{B}}, on {\partial\Omega\times[0,T]}. Then this result is applied to discuss the nature of the territorial refuges in periodic competitive environments.

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Linear Time-Periodic System Identification with Grouped Atomic Norm Regularization

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2020.12.1341 ◽

2020 ◽

Vol 53 (2) ◽

pp. 1237-1242

Author(s):

Mingzhou Yin ◽

Andrea Iannelli ◽

Mohammad Khosravi ◽

Anilkumar Parsi ◽

Roy S. Smith

Keyword(s):

System Identification ◽

Periodic System ◽

Linear Time ◽

Atomic Norm ◽

Time Periodic

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Identiﬁcation of Piecewise Constant Switching Linear Time-Periodic Systems

2020 28th Signal Processing and Communications Applications Conference (SIU) ◽

10.1109/siu49456.2020.9302100 ◽

2020 ◽

Author(s):

Ismail Uyanik

Keyword(s):

Linear Time ◽

Periodic Systems ◽

Piecewise Constant ◽

Time Periodic

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Identifying parameters of nonlinear structural dynamic systems using linear time-periodic approximations

Conference Proceedings of the Society for Experimental Mechanics Series - Modal Analysis Topics, Volume 3 ◽

10.1007/978-1-4419-9299-4_9 ◽

2011 ◽

pp. 103-126 ◽

Cited By ~ 1

Author(s):

Michael W. Sracic ◽

Matthew S. Allen

Keyword(s):

Dynamic Systems ◽

Linear Time ◽

Structural Dynamic ◽

Nonlinear Structural ◽

Time Periodic

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Periodic controller for guaranteed simultaneous stabilization of two plants with robust zero error tracking

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1177/0959651818797011 ◽

2018 ◽

Vol 233 (5) ◽

pp. 480-490

Author(s):

Arindam Chakraborty ◽

Jayati Dey

Keyword(s):

Design Methodology ◽

Linear Time ◽

Pole Placement ◽

Control Input ◽

Efficient Design ◽

Simultaneous Stabilization ◽

Bounded Control ◽

Linear Time Invariant ◽

Time Invariant ◽

Time Periodic

The guaranteed simultaneous stabilization of two linear time-invariant plants is achieved by continuous-time periodic controller with high controller frequency. Simultaneous stabilization is accomplished by means of pole-placement along with robust zero error tracking to either of two plants. The present work also proposes an efficient design methodology for the same. The periodic controller designed and synthesized for realizable bounded control input with the proposed methodology is always possible to implement with guaranteed simultaneous stabilization for two plants. Simulation and experimental results establish the veracity of the claim.

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