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This work presents a novel control approach that integrates backstepping and dynamic surface control techniques to design an H∞ tracking control system. Our focus is on a particular class of nonlinear systems that do not possess lower triangular structure, with a specific application to the coronary system. By employing dynamic surface control, the issue of differential explosion encountered during the backstepping process is effectively addressed, while also guaranteeing robustness. Finally, simulation of coronary artery system proves the effectiveness of the proposed control strategy.

The purpose of this paper is to address the problem of assessing the stability of singular time-varying delay systems. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, a model transformation using a three-terms approximation of the delayed state is exploited. Based on the lifting method and the Lyapunov–Krasovskii functional (LKF) method, a new linear matrix inequality (LMI) is obtained, allowing conclusions on stability to be drawn using the scaled small gain theorem (SSG). The use of SSG theorem for stability of singular systems with time-varying delay has not been investigated elsewhere in the literature. This represents the main novelty of this article. The result is applicable for assessing the stability of both singular systems and neutral systems with time-varying delays. The less conservativeness of the stability test is illustrated by comparison with recent literature results. [ABSTRACT FROM AUTHOR]