H? Control

H? control has been one of the popular methods for stabilizing dynamic systems with externally finite energy or power disturbance, and great attention has been paid to this problem. This chapter focuses on the mode-independent H? control problem for SMJSs. When the TRM can be selected, several sets of sufficient conditions in terms of LMIs with equation constraints are presented, where control gains can be obtained directly. When MDCs have OMs disordered, sufficient conditions for such disordered controllers are given in terms of LMIs. Without designing NOM-dependent controller directly, a kind of controller only related to OOMs is developed. Especially, another method for designing an MIC is given, which requires that the state transition probability is known exactly. In the case when the state transition probability is unaccessible or unavailable, a unified approach to H? control problem is developed in the LMI setting, where the TRM can be uncertain, partially unknown and designed, and both H? MIC and MDCs are obtained simultaneously. Based on these methods, improved results in terms of considering the probabilities of MIC and MDCs taking place are presented. The available probability of system mode described by a Bernoulli variable is taken into account, which plays an important role in system design. Finally, an adaptive controller is developed to deal with a general case when the probability is inaccessible. All these conditions are expressed in terms of LMIs, and thus they can be solved easily using the existing software package.