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dc.contributor.authorAlwan, Mohamad
dc.date.accessioned2011-09-02 18:06:26 (GMT)
dc.date.available2011-09-02 18:06:26 (GMT)
dc.description.abstractHybrid systems with or without stochastic noise and with or without time delay are addressed and the qualitative properties of these systems are investigated. The main contribution of this thesis is distributed in three parts. In Part I, nonlinear stochastic impulsive systems with time delay (SISD) with variable impulses are formulated and some of the fundamental properties of the systems, such as existence of local and global solution, uniqueness, and forward continuation of the solution are established. After that, stability and input-to-state stability (ISS) properties of SISD with fixed impulses are developed, where Razumikhin methodology is used. These results are then carried over to discussed the same qualitative properties of large scale SISD. Applications to automated control systems and control systems with faulty actuators are used to justify the proposed approaches. Part II is devoted to address ISS of stochastic ordinary and delay switched systems. To achieve a variety stability-like results, multiple Lyapunov technique as a tool is applied. Moreover, to organize the switching among the system modes, a newly developed initial-state-dependent dwell-time switching law and Markovian switching are separately employed. Part III deals with systems of differential equations with piecewise constant arguments with and without random noise. These systems are viewed as a special type of hybrid systems. Existence and uniqueness results are first obtained. Then, comparison principles are established which are later applied to develop some stability results of the systems.en
dc.publisherUniversity of Waterlooen
dc.subjectImpulsive systemsen
dc.subjectSwitched systemsen
dc.subjectStochastic differential equationsen
dc.subjectTime delayen
dc.subjectAsymptotic stabilityen
dc.subjectExponential stabilityen
dc.subjectLyapunov stabilityen
dc.subjectComparison principleen
dc.subjectRazumikhin techniqueen
dc.subjectExistence-uniqueness of solutionsen
dc.subjectDifferential equations with piecewise constant argumentsen
dc.titleQualitative Properties of Stochastic Hybrid Systems and Applicationsen
dc.typeDoctoral Thesisen
dc.subject.programApplied Mathematicsen
uws-etd.degree.departmentApplied Mathematicsen
uws-etd.degreeDoctor of Philosophyen

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