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Fractional order boundary controller enhancing stability of partial differential wave equation systems with delayed feedback

Shantanu Das


For a feedback systems introduction of small delays make the system unstable. The boundary control problem is very new phenomena studied widely, and time delay introduced in boundary feedback destabilizes the system, which otherwise is asymptotically stable in absence of delay. If the boundary controller be of “fractional” order does it give any advantage of enhanced robustness in presence of small delays in the boundary feedback; is studied here. The example of wave equation with boundary fractional order controller gives idea of enhanced stability when delay are present; gives encouraging result-thus fractional order controllers may be employed in such systems with distributed parameters defined by partial differential equation PDE (of integer or fractional order), with controller sitting at one boundary. The paper develops the mathematical basis for stability of PDE systems controlled by boundary controllers, via complex analysis.


Boundary Control System, Partial Differential Equation, Fractional Derivative, Stability, Wave Equation, Rouche’s Theorem, Spectral Radius.

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