#### Title

Stability Analysis of Jump-Linear Systems Driven by Finite-State Machines with Markovian Inputs

#### Date of Award

Summer 2004

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Electrical & Computer Engineering

#### Committee Director

W. Steven Gray

#### Committee Member

Oscar R. Gonzalez

#### Committee Member

Linda L. Vahala

#### Committee Member

Dayanand N. Naik

#### Abstract

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.

#### DOI

10.25777/dghh-yv38

#### ISBN

9780496076093

#### Recommended Citation

Patilkulkarni, Sudarshan S..
"Stability Analysis of Jump-Linear Systems Driven by Finite-State Machines with Markovian Inputs"
(2004). Doctor of Philosophy (PhD), Dissertation, Electrical & Computer Engineering, Old Dominion University, DOI: 10.25777/dghh-yv38

https://digitalcommons.odu.edu/ece_etds/118

#### Included in

Aerospace Engineering Commons, Electrical and Computer Engineering Commons, Systems Engineering Commons