This study aims to design a robust state feedback controller for uncertain and perturbed linear systems with state constraints described by a polytope. This novel design incorporates the use of a composite barrier Lyapunov function (CBLF) and the convex hull of a set of ellipsoids inscribed in the given polytopic constraint set. The CBLF is used to ensure that this convex hull is an invariant set for the perturbed system states. Then, an optimization scheme is implemented to maximize the size of this invariant set to use it as a safe set. This is a set of initial conditions ensuring that the system solutions conform to the constraints for any subsequent time instant. Additionally, a minimal ultimate bound for the states is calculated to ensure asymptotic convergence to a region as close to the origin as possible. This region is characterized by a second convex hull of ellipsoids using the well-known attractive ellipsoid method and the CBLF. Numerical simulations illustrate and compare the obtained results against a similar approach, considering the classical quadratic Lyapunov function, instead of the CBLF.

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This study intends to present an automatic control design for a Cartesian electrospinning system with a dual moving platforms for the collector and the syringe subsystems which are mobilized using linear actuators. The proposed device is including a set of dual robotized structures, that is also carrying a structure to create the Taylor cone that regulates the nano-fiber deposition over the supporting platform. The suggested control form considers the synchronization between the syringe tip and the collector using a cascade tracking structure. A class of distributed state-dependent terminal sliding mode control form solves the tracking problem that yields the syringe-collector pair moves in a synchronized form tracking a bidimensional design that should be reproduced with the fibers deposition made of polyvinyl acid–based polymer. This controller also considers the working space restrictions in the Cartesian electrospinning system device using state-dependent gains which are obtained using a control barrier Lyapunov function. The application of the second stability method of Lyapunov serves to both design the state-dependent gains and prove that the tracking error trajectory is ultimate bound. The proposed controller is evaluated using a cyber-physical representation of the Cartesian electrospinning system device where the proposed controller is evaluated. This evaluation considers a comparison of the control effectiveness (using the root mean square value of the tracking error) with a traditional non-adaptive state feedback and a first-order sliding mode control. This comparison shows that the proposed adaptive controller induces the smallest root mean square among the tested control forms while reducing the magnitude of the overshoot for each actuator.

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