This monograph is an up-to-date presentation of the analysis and design
of singular Markovian jump systems (SMJSs) in which the transition rate
matrix of the underlying systems is generally uncertain, partially
unknown and designed. The problems addressed include stability,
stabilization, H∞ control and filtering, observer design, and adaptive
control. applications of Markov process are investigated by using
Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the
stochastic Barbalat's Lemma, among other techniques.
Features of the book include:
- study of the stability problem for SMJSs with general transition rate
matrices (TRMs);
- stabilization for SMJSs by TRM design, noise control,
proportional-derivative and partially mode-dependent control, in terms
of LMIs with and without equation constraints;
- mode-dependent and mode-independent H∞ control solutions with
development of a type of disordered controller;
- observer-based controllers of SMJSs in which both the designed
observer and controller are either mode-dependent or mode-independent;
- consideration of robust H∞ filtering in terms of uncertain TRM or
filter parameters leading to a method for totally mode-independent
filtering
- development of LMI-based conditions for a class of adaptive state
feedback controllers with almost-certainly-bounded estimated error and
almost-certainly-asymptotically-stable corresponding closed-loop system
states
- applications of Markov process on singular systems with norm bounded
uncertainties and time-varying delays
Analysis and Design of Singular Markovian Jump Systems contains
valuable reference material for academic researchers wishing to explore
the area. The contents are also suitable for a one-semester graduate
course.
