This book considers a number of important aspects for the analysis of fault tolerant control systems (FTCS). An FTCS is a collection of techniques which provide of systematic approach to maintain system stability and acceptable performance not only during normal system operation, but also in the presence of system component malfunctions. Based on the available resources of system redundancy, the design approaches of FTCS can be classified into passive and active. It is the objective of this book to analyze the stochastic behaviour of active FTCS (AFTCS).
AFTCS relies on a fault detection and identification process to monitor system perfomance, and to detect and isolate faults in the system. The dynamic behaviour of AFTCS can be modelled by a Stochastic Differential Equation (SDE), which can be classified into two categories: SDE perturbed by white Gaussian noise (Ito SDE) and SDE whose coefficients vary randomly with Markovian characteristics (hybrid systems). Substantial results for the stability of hybrid systems are obtained using the Lyapunov function approach and the supermartingale property. The class of hybrid systems known as FTCS with Markovian Parameters (FTCSMP) is considered.
The book adopts the Lyapunov second (direct) method to characterize the behaviour of FTCSMP without explicit solution of the SDE. A prime focus of the book is the stochastic stability of FTCSMP. In particular, exponential stability, mean square and almost sure asymptotic stability are investigated. All theoretical results are validated by simulation examples. Applications of the presented results to practical systems are discussed.