This paper investigates the finite-time boundedness (FTB) and robust control of switched linear systems with unstable systems (SLS-US) by utilizing mode-dependent average dwell time (MDADT). Due to the consideration of the presence of unstable subsystems in our work, this paper distinguishes between switching signals in stable and unstable cases based on the characteristic of allowing each subsystem to have independent average dwell time (ADT) according to MDADT. Stable subsystems utilize slow MDADT (SMDADT), whereas unstable subsystems employ fast MDADT (FMDADT). This switching behaviour effectively addresses the energy increment caused by the divergence of unstable systems. This paper presents the necessary conditions to achieve the H∞ performance index within the SLS-US. Moreover, it outlines the design of a state-feedback controller aimed at resolving the H∞ control problem within the closed-loop system. The verification of the proposed result is conducted through linear matrix inequalities (LMIs). Finally, the paper confirms the practicality of the proposed theory.
KEYWORDS: Switching, Matrices, Darmstadtium, Telecommunications, Computing systems, Analytical research, Ultraviolet radiation, Design, Control systems design, Control systems
The research purpose of uncertain time-varying delays (T-V Ds) switching systems is mainly to analyse stability of systems, design suitable controllers, and apply them to practical engineering problems. In this article, a issue of robust stability analysis is formulated for a kind of uncertain switched systems (SSs) with linear T-V Ds. Firstly, robust stabilities norm for SSs are obtained by establishing suitable multiple Lyapunov-Krasovskii functionals (MLKF) along with the application of a mode-dependent average dwell time (MDADT) switching approach. Second, research determines the robust stabilities of uncertain non-switching systems through the solution of linear matrix inequalities (LMIs). Building upon the approach, this research extends the robust stability analysis to uncertain SSs with T-V Ds. Lastly, simulation instances are suggested to prove the efficiency and validity of our theoretic findings. This article can better understand the impact of these phenomena on system stability and propose effective control strategies to enhance system stability. With the continuous deepening of research and technological innovation, it is expected to see more application achievements based on uncertain time-delay switching systems in the future.
Switching systems offer an efficient approach for modeling and controlling intricate systems, and their associated topics have garnered significant attention in the realm of control research. Current research pertaining to the analysis of stability and the development of controllers for these systems often relies on methods such as dwell time or state feedback, which can lead to unnecessary switching and control actions. However, the event-triggered control method can effectively minimize the frequency of communication and control, thereby conserving valuable communication and computational resources. In light of this, an error-type event triggering mechanism(ETM) and state-dependent switching signal(STSS) are proposed for a kind of actuator nested saturation(NES) switching system, and compared with the mode-dependent average dwell time(MDADT) switching method, the advantage of excluding Zeno phenomenon without calculation is obtained. The technique of multiple Lyapunov functions(MLF) ensures stability by fulfilling the required conditions of the local exponential stability(LES) of the switched system(SCHS) and related inferences. The ultimate validation of the proposed method's efficiency comes through simulation examples. The approach introduced in this paper considers both the cost of switching and non-intrusive switching performance while minimizing the number of switches. Furthermore, a plan for achieving stable and effective switching in NES systems is outlined.
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