Robust guaranteed cost control for a class of perturbed systems with multiple distributed time delays. (August 2019) - Rodríguez-Guerrero, Liliam; Cuvas-Castillo, Carlos; Santos-Sánchez, Omar-Jacobo; Ordaz-Oliver, Jesús-Patricio; García-Samperio, César-Arturo
Highlights: It is presented a robust guaranteed cost control for perturbed systems with multiple distributed time delays. With the complete type functional approach, the existence of the control is always guaranteed only using standard majorizations. A new algorithm for computing the gains of a linear state feedback control, based on LMI is provided. The control law is programmed and tested on the industrial Programable Automatic Controller NI cDAQ-9132, to regulate the temperature on a dehydration process. Satisfactory experimental results demonstrated the feasibility of our proposal. Abstract: In this paper, a robust guaranteed cost control is designed for linear systems with multiple pointwise and distributed state delays, when it is considered the presence of a perturbation that satisfies the matching condition. This result is carried out by combining a complete type Lyapunov-Krasovskii functional, a quadratic cost function, and the Lyapunov redesign technique. The obtained nonlinear state feedback is composed by three control laws: the first one stabilizes the nominal system (a new algorithm is presented), the second one is such that an upper bound of a cost function is guaranteed, and the last one compensates the perturbation effects, ensuring the robust stability of the closed loop system. In order to validate the proposal, numerical simulations are presented, and the controller is applied to regulate a real time dehydration process temperature, implemented on an industrial Programable Automatic Control NI cDAQ − 9132.