The technical note is concerned with the stabilization problem of networked control systems. A general framework is proposed firstly, where the zero-order hold has the logical capability of choosing the newest control input packet. The continuous-time process is discretized as a system with input delays. Then a sufficient condition for testing the stability of the discretized system and two sufficient conditions for designing a stabilizing controller are established based upon the Lyapunov theory. Finally numerical examples and simulations are used to illustrate the developed theory.

The note is concerned with linear negative imaginary systems. First, a previously established Negative Imaginary Lemma is shown to remain true even if the system transfer function matrix has poles on the imaginary axis. This result is achieved by suitably extending the definition of negative imaginary transfer function matrices. Secondly, a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems. Meanwhile, some properties of linear negative imaginary systems are developed. Finally, an undamped flexible structure example is presented to illustrate the theory.

This article deals with the robust H ₂ control problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertainties under consideration appear both in the system parameters and in the mode transition rates. First, a new criterion based on linear matrix inequalities is established for checking the robust H ₂ performance of the uncertain system. Then, a sufficient condition for the existence of the state-feedback controllers is established such that the closed-loop system is quadratically mean square stable and has a certain level of robust H ₂ performance in terms of linear matrix inequalities with equality constraints. A globally convergent algorithm is also presented to construct such controllers effectively. Finally, an illustrative numerical example is used to demonstrate the developed theory.