Date of Award

Summer 2004

Document Type


Degree Name

Doctor of Philosophy (PhD)


Electrical & Computer Engineering

Committee Director

W. Steven Gray

Committee Member

Oscar R. Gonzalez

Committee Member

Linda L. Vahala

Committee Member

Dayanand N. Naik


A control system with a fault recovery mechanism in the feedback loop and with faults occurring in a non-deterministic manner can be modeled as a class of hybrid systems, i.e., a dynamical system switched by a finite-state machine or an automaton. When the plant and controller are linear, such a system can be modeled as a jump-linear system driven by a finite-state machine with a random input process. Such fault recovery mechanisms are found in flight control systems and distributed control systems with communication networks. In these critical applications, closed-loop stability of the system in the presence of fault recoveries becomes an important issue.

Finite-state machines as mathematical constructs are widely used by computer scientists to model and analyze algorithms. In particular, fault recovery mechanisms that are implemented in hardware with logic based circuits and finite memory can be modeled appropriately with finite-state machines. In this thesis, mathematical tools are developed to determine the mean-square stability of a closed-loop system, modeled as a jump-linear system in series with a finite-state machine driven by a random process. The random input process is in general assumed to be any r-th order Markov process, where r ≥ 0. While stability tests for a jump-linear system with a Markovian switching rule are well known, the main contribution of the present work arises from the fact that output of a finite-state machine driven by a Markov process is in general not Markovian. Therefore, new stability analysis tools are provided for this class of systems and demonstrated through Monte Carlo simulations.


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