Date of Award

Winter 2006

Document Type


Degree Name

Doctor of Philosophy (PhD)


Electrical & Computer Engineering


Electrical Engineering

Committee Director

Oscar R. Gonzalez

Committee Member

Victor A. Carreno

Committee Member

N. Rao Chaganty

Committee Member

W. Steven Gray

Committee Member

Vishnu K. Lakdawala


In the past two decades, the number of applications that make use of supervisory algorithms to control complex continuous-time or discrete-time systems has increased steadily. Typical examples include air traffic management, digital control systems over networks, and flexible manufacturing systems. A common feature of these applications is the intermixing of the continuous dynamics of the controlled plant with the logical and discrete dynamics of the supervising algorithms. These so-called hybrid systems are the focus of much ongoing research. To improve the performance of these systems, it is important to analyze the interactions between the supervising algorithms and the plant. Few papers have studied this interaction when the plant is represented by a discrete-time system. Thus, this dissertation fixes this deficiency by addressing the following three main objectives: to introduce a new modeling framework for discrete-time stochastic hybrid systems suitable for stability analysis; to derive testable stability conditions for these models; and to demonstrate that these models are suitable to study real-world applications. To achieve the first objective, the Hybrid Jump Linear System model is introduced. Although it has many of the same modeling capabilities as other formalisms in the literature (e.g., Discrete Stochastic Hybrid Automata), it possesses the unique advantage of representing the dynamics of both the controlled plant and the supervising algorithm in the same analytical framework: stochastic difference equations. This enables the study of their joint properties such as, for example, mean square stability. The second objective is addressed by developing a collection of testable sufficient mean square stability conditions. These tests are developed by applying, successively, switched systems' techniques, singular value analysis, a second moment lifting technique, and Mark off kernel methods. The final objective is achieved by developing a hybrid jump linear system model of an AFTI-F16 flight controller deployed on a fault tolerant computer with rollback and cold-restart capabilities, and analyzing its stability properties.


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