|dc.description.abstract||A singular system model is mathematically formulated as a set of coupled differential
and algebraic equations. Singular systems, also referred to as descriptor or differential
algebraic 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 for
singular hybrid systems with or without time delay.
First, some su cient conditions on the exponential stability property of both continuous
and discrete impulsive switched singular systems with time delay (ISSSD) are proposed.
We address this problem for the continuous system in three cases: all subsystems are
stable, the system consists of both stable and unstable subsystems, and all subsystems are
unstable. For the discrete system, we focus on when all subsystems are stable, and the
system consists of both stable and unstable subsystems. The stability results for both the
continuous and the discrete system are investigated by first using the multiple Lyapunov
functions along with the average-dwell time (ADT) switching signal to organize the jumps
among the system modes and then resorting the Halanay Lemma.
Second, an optimal feedback control only for continuous ISSSD is designed to guarantee
the exponential stability of the closed-loop system. Moreover, a Luenberger-type observer
is designed to estimate the system states such that the corresponding closed-loop error
system is exponentially stable. Similarly, we have used the multiple Lyapunov functions
approach with the ADT switching signal and the Halanay Lemma.
Third, the problem of designing a sliding mode control (SMC) for singular systems
subject to impulsive effects is addressed in continuous and discrete contexts. The main
objective 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 eliminate
Last, mean square admissibility for singular switched systems with stochastic noise in
continuous and discrete cases is investigated. Sufficient conditions that guarantee mean
square admissibility are developed by using linear matrix inequalities (LMIs).||en