Stability analysis and controller design for a class of T-S fuzzy Markov jump system with uncertain expectation of packet dropouts

This paper is concerned with an H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> control for a class of Takagi-Sugeno (T-S) fuzzy Markov jump system under unreliable communication links. It is assumed that the transition probabilities determining the dynamical behavior of the underlying system are partially unknown and the communication links between the plant and the controller are imperfect (the packet dropouts occur intermittently). In this paper, a more practical scenario is considered in the setting, i.e., the expectation of packet losses represented as a description of Bernoulli-distributed stochastic process is uncertain. Attention is focused on the design of H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> controllers such that the closed-loop system is stochastically stable and preserves a guaranteed H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> performance. Based on basis-dependent Lyapunov function, the solutions to the problem are formulated in the form of linear matrix inequalities. An illustrative example is provided to demonstrate the effectiveness and applicability of the proposed theoretical results.