Abstract
This work discuss the robust stabilization problem for discrete-time switched singular systems with simultaneous presence of time-varying delay and sensor nonlinearity. To this end, an observer-based controller was synthesized that works under asynchronous switching signals. Investigating the average dwell time approach and using a Lyapunov–Krasovskii functional with triple sum terms, sufficient conditions were derived for achieving the existence of such asynchronous controller and guaranteeing the resulting closed-loop system to be exponentially admissible with H∞ performance level. Subsequently, the effectiveness of the proposed control scheme was verified through two numerical examples.
Highlights
Great interest has been devoted to the study of switched singular systems on both theoretical and application fronts ([1,2,3], and the references therein)
From a mathematical point of view, switched singular systems are typically each composed of a finite number of subsystems and a switching law that specifies the active subsystems at each instant of time
All the montioned works are concerned with arbitrary switching signal to study switched singular systems
Summary
Great interest has been devoted to the study of switched singular systems on both theoretical and application fronts ([1,2,3], and the references therein). The SVD technique is difficult to use when the disturbance affects the measurements and the use of an iterative algorithm such the CCL can complicate the resolution of LMI conditions In this regard, how to deal with dynamic systems with unavailable states for measurement by using an observer-based controller for the considered system under asynchronous switching was the second motivation for this work. The sensor saturation effect has not been investigated when dealing with the problem of asynchronous ADT observer-based control for discrete-time switched singular systems with time-varying delay. This represents the third motivation for this paper. If their dimensions are not explicitly stated, are assumed to be compatible for algebraic operations. k.k denotes the Euclidean norm of a vector and its induced norm of a matrix. col {Y, X } denotes a column matrix
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