Estimation for Fuzzy Semi-Markov Jump Systems With Indirectly Accessible Mode Information and Nonideal Data Transmission

Abstract

This article proposes a novel <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> state estimation scheme for a family of Takagi-Sugeno fuzzy semi-Markov jump systems with indirectly accessible mode information and nonideal data transmission. To address estimation of the indirectly accessible modes, the observed-mode sequence emitted by emission probabilities is utilized in this article. By extending the classic Lyapunov stability theory, a set of novel convex stability criteria is proposed by eliminating the nonconvex terms in stabilization conditions with the aid of certain techniques. The proposed stability criteria are utilized to ensure the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance of the studied fuzzy systems. In addition, numerically checkable conditions on the existence of a fuzzy observed-mode-dependent estimator are formulated to guarantee the σ-error mean square stability of the underlying error system with a guaranteed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> disturbance attenuation level. The developed theoretical results are illustrated by an application of a single-link robotic arm.