Abstract
This paper presents Linear Matrix Inequalities (LMIs) conditions for designing Proportional-Integral-Derivative (PID) controllers that guarantee asymptotic stability with exponential convergence rate for positioning systems affected by hysteresis nonlinearity and time-varying delay. The hysteresis is modelled using the Prandtl-Ishlinskii operator, and the effects of both the time-varying delay and hysteresis are encapsulated into a bounded uncertain parameter confined within a known convex polytope. Numerical results support the theoretical developments, confirming that the controller effectively mitigates the effects of disturbances while suppressing both the hysteresis and time-varying delay influences.
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