Qualitative Properties of Hybrid Singular Systems

Singular Systems;Hybrid Systems;Stability;Sliding Mode Control;Stochastic Singular Systems;Feedback Control

Kiyak, Humeyraadvisor:Liu, Xinzhi ; affiliation1:Faculty of Mathematics ; Liu, Xinzhi ;

University of Waterloo

关键词: Feedback Control;    Hybrid Systems;    Sliding Mode Control;    Stability;    Stochastic Singular Systems;    Singular Systems;    Doctoral Thesis;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/14351/4/kiyak_humeyra.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

A singular system model is mathematically formulated as a set of coupled differentialand algebraic equations. Singular systems, also referred to as descriptor or differentialalgebraic systems, have extensive applications in power, economic, and biological systems.The main purpose of this thesis is to address the problems of stability and stabilization forsingular hybrid systems with or without time delay.First, some su cient conditions on the exponential stability property of both continuousand discrete impulsive switched singular systems with time delay (ISSSD) are proposed.We address this problem for the continuous system in three cases: all subsystems arestable, the system consists of both stable and unstable subsystems, and all subsystems areunstable. For the discrete system, we focus on when all subsystems are stable, and thesystem consists of both stable and unstable subsystems. The stability results for both thecontinuous and the discrete system are investigated byfirst using the multiple Lyapunovfunctions along with the average-dwell time (ADT) switching signal to organize the jumpsamong the system modes and then resorting the Halanay Lemma.Second, an optimal feedback control only for continuous ISSSD is designed to guaranteethe exponential stability of the closed-loop system. Moreover, a Luenberger-type observeris designed to estimate the system states such that the corresponding closed-loop errorsystem is exponentially stable. Similarly, we have used the multiple Lyapunov functionsapproach with the ADT switching signal and the Halanay Lemma.Third, the problem of designing a sliding mode control (SMC) for singular systemssubject to impulsive effects is addressed in continuous and discrete contexts. The mainobjective is to design an SMC law such that the closed-loop system achieves stability.Designing a sliding surface, analyzing a reaching condition and designing an SMC law are investigated throughly. In addition, the discrete SMC law is slightly modi ed to eliminatechattering.Last, mean square admissibility for singular switched systems with stochastic noise incontinuous and discrete cases is investigated. Sufficient conditions that guarantee meansquare admissibility are developed by using linear matrix inequalities (LMIs).