Stability Analysis and Stabilization of Time-Delay Switching Systems Using the Non-Monotonic Lyapunov–Krasovskii Technique

نوع: Type: Thesis

مقطع: Segment: maters

عنوان: Title: Stability Analysis and Stabilization of Time-Delay Switching Systems Using the Non-Monotonic Lyapunov–Krasovskii Technique

ارائه دهنده: Provider: Saeed Ahmadi

اساتید راهنما: Supervisors: Dr. Younes Salgi, Dr. Seyed Manouchehr Hosseini PilanGorgi

اساتید مشاور: Advisory Professors:

اساتید ممتحن یا داور: Examining professors or referees: Dr. Razieh Torkamani, Dr. Ali Kalantarnia

زمان و تاریخ ارائه: Time and date of presentation: 2026

مکان ارائه: Place of presentation: 33

چکیده: Abstract: The importance of stability analysis and stabilization of switching systems with time delays is well recognized, as the presence of delays and switching among subsystems can significantly affect the stability and performance of such systems. Consequently, numerous studies have focused on the stability of discrete-time switching systems with time delays. In most previous works, stability analysis has been based on the conventional Lyapunov–Krasovskii technique, which requires the uniform decrease of the Lyapunov function at each time step. This stringent requirement reduces the flexibility of the method and, in many cases, leads to conservative conditions, particularly in the presence of time delays and stochastic switching phenomena.In this study, to overcome the aforementioned limitations, a novel and efficient approach based on a nonuniform Lyapunov–Krasovskii technique is proposed for the stability analysis and stabilization of linear discrete-time switching systems with time delays. Within this framework, the uniform decrease requirement of the Lyapunov function is replaced with nonuniform conditions. Moreover, the stability of the system is analyzed not only over a limited number of time steps but also over an m-step horizon, without restricting the analysis to only a few time instants. To this end, a set of sufficient conditions in the form of linear matrix inequalities (LMIs) is derived, enabling the stability assessment of switching systems with time delays.This method also facilitates the design of stabilization algorithms. Accordingly, a state-feedback controller with input delay is designed and integrated with an event-triggered control (ETC) mechanism. In this way, an event-triggered control scheme within the nonuniform Lyapunov–Krasovskii framework is introduced and analyzed for a specific class of linear discrete-time switching systems with input delays. This integration reduces the need for continuous updates at every time step, thereby saving computational and communication resources. The effectiveness and reduced conservatism of the proposed stability analysis and stabilization methods are demonstrated through several examples and numerical simulations