ABSTRACT
This chapter investigates the infinite horizon H2/H∞ control for linear discrete time-varying (LDTV) systems and develops some essential theories on time-varying systems with multiplicative noise, including detectability, observability and properties of GLEs. It presents exact detectability of the stochastic system, from which it can be found that there are some essential differences between time-varying and time-invariant systems. In addition, Lyapunov-type theorems are also presented. It can be found that for LDTV stochastic systems, there are many different properties from linear time-invariant systems, especially in detectability and spectral characterization for stability. Up to now, there is almost no similar result to that of on the study of stability, observability and detectability of LDTV stochastic systems based on the spectrum technique of infinite dimensional operators. There exist many issues that require further research.
