Control of time-delayed Markovian jump linear systems

Motivated by networked control systems, a class of Markovian jump linear switching systems with time-delays that are random is considered. Unlike assumptions made in traditional control theory, network control systems no longer assumes that information or signals exchanged between subsystems (or components) are ideal or perfect. Indeed, imperfect information exchanges such as unexpected delays and partial or total loss of information make the network control systems unique and difficult to deal with. Fortunately, it is known that a Markovian jump linear system is an appropriate mathematical representation of the systems with sudden changes of dynamical behavior. For this reason, the mathematical framework considered in this thesis is Markovian jump linear systems with time-delays. Conditions for stability of the Makovian jump linear systems with time-delays that are fixed and known apriorly are first developed. The condition is extended to a stabilizability condition that enables the formulation of a control design algorithm. The controller designed is a state feedback which depends on the switching mode of the Markovian jump linear system to be controlled, and guarantees stochastic stability of the overall system. The results are further extended to deal with the case when the plant to be controlled is uncertain. Given the assumption that the plant\u27s uncertainty is described in terms of a bounded norm, a control design technique is developed to compute a state feedback controller that ensures the stochastic stability of the overall system under the prescribed plant perturbations. The case when the time-delay is random, time-varying, and unknown is considered next. Stability and stabilizability conditions for such systems have been derived and subsequently the control design algorithm has been obtained. An algorithm to compute a robust controller for the uncertain system is also developed. The results obtained are all depending on the switching mode of the Markovian jump linear switching systems, but independent from the delay. Better and sharper results are expected from the conditions depending on delay. Motivated by this, stability, stabilizability, and robust stabilizability conditions that are functions of time-delay presented in the system are developed. Each condition developed is in the form of Linear Matrix Inequalities that can be efficiently solved by standard computational tools such as Matlab. Each condition is also illustrated by an example. A systems engineering approach is employed and used to implement and verify the subsystems design for Markovian Jump Linear Systems with time-varying delays for a network control system