CONTROL OF INTERCONNECTED JUMPING SYSTEMS: AN H_∞ APPROACH

Abstract

This paper investigates, by using an H ∞ approach, the problems of stochastic stability and control for a class of interconnected systems with Markovian jumping parameters. Both cases of finite-and infinite-horizon are studied. It is shown that the problems under consideration can be solved if a set of coupled differential or algebraic Riccati equations are solvable.

Interconnected jumping time‐delay systems: Mode‐dependent decentralized stability and stabilization

“…When the interconnected system involves delays, related studies are reported in 3, 4. Markovian jump linear systems are a special class of hybrid systems with both modes and state variables 9–13. This class of systems can model physical systems with abrupt structural changes accurately, such as failure prone manufacturing systems, power systems and economics systems.…”

Decentralized $\mathcal{L}_{2}$ – $\mathcal{L}_{\infty}$ Filtering for Interconnected Markovian Jump Systems with Delays

“…A few of valuable results on the decentralized control problem for interconnected Markovian jump systems have been available. In [15], the authors considered the decentralized H ∞ state-feedback control problem and showed that this problem could be solved if a set of coupled differential or algebraic Riccati equations were solvable. The state-feedback and output-feedback absolute stabilization problems for uncertain interconnected Markovian jump systems were studied in [9] and [25], respectively, where necessary and sufficient conditions for the solvability of the considered problems were presented by means of generalized algebraic Riccati equations.…”