Analysis and synthesis of Markov Jump Linear systems with time-varying delays and partially known transition probabilities

In this note, the stability analysis and stabilization problems for a class of discrete-time Markov jump linear systems with partially known transition probabilities and time-varying delays are investigated. The time-delay is considered to be time-varying and has a lower and upper bounds. The transition probabilities of the mode jumps are considered to be partially known, which relax the traditional assumption in Markov jump systems that all of them must be completely known a priori. Following the recent study on the class of systems, a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix. Sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality (LMI) formulation, and the design of the stabilizing controller is further given. A numerical example is used to illustrate the developed theory. © 2008 IEEE.published_or_final_versio

Adaptive Controller Placement for Wireless Sensor-Actuator Networks with Erasure Channels

Wireless sensor-actuator networks offer flexibility for control design. One novel element which may arise in networks with multiple nodes is that the role of some nodes does not need to be fixed. In particular, there is no need to pre-allocate which nodes assume controller functions and which ones merely relay data. We present a flexible architecture for networked control using multiple nodes connected in series over analog erasure channels without acknowledgments. The control architecture proposed adapts to changes in network conditions, by allowing the role played by individual nodes to depend upon transmission outcomes. We adopt stochastic models for transmission outcomes and characterize the distribution of controller location and the covariance of system states. Simulation results illustrate that the proposed architecture has the potential to give better performance than limiting control calculations to be carried out at a fixed node.Comment: 10 pages, 8 figures, to be published in Automatic

Preview Tracking Control of Linear Periodic Switched Systems with Dwell Time

This paper studies the preview tracking control problem for linear discrete-time periodic switched systems. Firstly, an augmented error system is constructed for each subsystem by stabilizing the augmented error systems through the method of optimal preview control, and the tracking problem of the switched system is transformed into the switched stability problem of closed-loop augmented error systems. Secondly, a switched Lyapunov function method is applied to search the minimal dwell time satisfying the switched stability of the closed-loop augmented error systems. Thirdly, the switched preview control input is solved from the controller of the individual augmented error system, and then the sufficient conditions and the preview controller can be obtained to guarantee the solvability of the original periodic switched preview tracking problem. Finally, numerical simulations show the effectiveness of the stabilization design method