This book gives an introduction to H-infinity and H2 control for linear
time-varying systems. Chapter 2 is concerned with continuous-time
systems while Chapter 3 is devoted to discrete-time systems.
The main aim of this book is to develop the H-infinity and H2 theory for
jump systems and to apply it to sampled-data systems. The jump system
gives a natural state space representation of sampled-data systems, and
original signals and parameters are maintained in the new system. Two
earlier chapters serve as preliminaries. Chapter 4 introduces jump
systems and develops the H-infinity and H2 theory for them. It is then
applied to sampled-data systems in Chapter 5.
The new features of this book are as follows: The H-infinity control
theory is developed for time-varying systems with initial uncertainty.
Recent results on the relation of three Riccati equations are included.
The H2 theory usually given for time-invariant systems is extended to
time-varying systems. The H-infinity and H2 theory for sampled-data
systems is established from the jump system point of view. Extension of
the theory to infinite dimensional systems and nonlinear systems is
discussed. This covers the sampled-data system with first-order hold. In
this book 16 examples and 40 figures of computer simulations are
included.
The reader can find the H-infinity and H2 theory for linear time-varying
systems and sampled-data systems developed in a unified manner. Some
arguments inherent to time varying systems or the jump system point of
view to sampled-data systems may give new insights into the system
theory of time-invariant systems and sampled-data systems.