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This paper presents new stabilization conditions for discrete-time linear parameter-varying systems in the form of linear matrix inequalities. The use of Lyapunov functions with dependence on delayed scheduling parameters is introduced. In addition, a lifted condition based on a Lyapunov function with dependence on delayed scheduling parameters, constructed in terms of an augmented state vector that takes into account a generic number of higher-order shifted states, is presented. Numerical examples are provided to illustrate the advantages of the proposed approach when compared to other techniques from the literature.

Over the past few decades, interval arithmetic has been attracting widespread interest from the scientific community. With the expansion of computing power, scientific computing is encountering a noteworthy shift from floating-point arithmetic toward increased use of interval arithmetic. Notwithstanding the significant reliability of interval arithmetic, this paper presents a theoretical inconsistency in a simulation of dynamical systems using a well-known implementation of arithmetic interval. We have observed that two natural interval extensions present an empty intersection during a finite time range, which is contrary to the fundamental theorem of interval analysis. We have proposed a procedure to at least partially overcome this problem, based on the union of the two generated pseudo-orbits. This paper also shows a successful case of interval arithmetic application in the reduction of interval width size on the simulation of discrete map. The implications of our findings on the reliability of scientific computing using interval arithmetic have been properly addressed using two numerical examples.

This article proposes a data-stream-driven event-triggered control strategy using evolving fuzzy models learned by granulation of input-output samples of nonlinear systems with unknown time-varying dynamics. The evolving fuzzy model is obtained online from a data stream ensuring data coverage based on the principle of justifiable granularity and controlled by an event-triggering learning mechanism dependent on the model accuracy. This evolving fuzzy model is used to design event-triggered fuzzy controller to stabilize networked control systems while reducing the used communication resources. The event-triggered learning mechanism is employed to determine the instants in which the event-triggered fuzzy controller should be redesigned. Numerical examples illustrate the effectiveness of the proposed learning event-triggered fuzzy control algorithm.