Stabilization Of Discrete-time Markovian Jump Systems Based On LMI

A large class of physical systems has variable structures subject to random changes, which result from the abrupt phenomena such as component and inter-connection failures or random communication delays in automobile vehicles. The state of such systems is driven by times and events. The state space of them' contains both continuous-valued states that take values from a Euclidean vector space Rn and discrete-valued states that take values from a discrete finite set S. The transitions between the different regimes have to be considered as random; in other words, and the dynamics of the discrete states are given by a Markovian jump process. Systems with this character may be modeled as Markovian jump systems. Nowadays more and more people have paid attention to the stability analysis of the Markovian jump systems and the study of the switching control. This dissertation devotes to the analysis of the stability of several kinds of the closed-loop systems. The main contents are as follows:1. The stabilization problem of a class of Markovian jump linear systems over networks via a random communication time-delayed controller and an impulsive controller is discussed. The random communication delays in the model signal are modeled as a Markov chain. First, we introduce a hybrid controller with delay and. impulses for the networked control systems. Then, some sufficient conditions are proposed for the design of a hybrid controller such that the closed-loop system is stochastically stable.2. The stabilization problem of the discrete-time Markovian jump linear sys-tems with time-delayed controller under partly unknown transition probabilities is investigated. Time-delays are both contained in the system states and in the mode signal. In contrast to the systems with completely known and completely unknown transition probabilities, the systems studied are more general. The suf-ficient conditions are derived via LMIs formulation for the design of a controller such that the closed-loop systems are stochastically stable.3. For a class of discrete-time nonlinear stochastic uncertain systems with missing measurements, its robust H∞filtering problem has been studied. The coefficients in the systems are modeled as a Markov chain. It is assumed that the uncertain matrices are norm bounded, and furthermore, the external disturbance is a stochastic process, and the missing measurements are described by a binary switching sequence that obeys a conditional probability distribution. The problem addressed is the design of an output feedback controller such that, for all admissible uncertainties, the resulting closed-loop system is exponentially stable in the mean square for the zero disturbance input and also achieve a prescribed H∞performance level. By using the Lyapunov method and stochastic analysis techniques, sufficient conditions are first derived to guarantee the existence of the desired controllers, and then the controller parameters are characterized in terms of linear matrix inequalities.