Abstract
Considering some unmeasurable states, a fuzzy static output control problem of nonlinear stochastic systems is discussed in this paper. Based on a modelling approach, a Takagi–Sugeno (T–S) fuzzy system, constructed by a family of stochastic differential equations and membership functions, is applied to represent nonlinear stochastic systems. Parallel distributed compensation (PDC) technology is used to construct the static output controller. A line-integral Lyapunov function (LILF) is used to derive some sufficient conditions for guaranteeing the asymptotical stability in the mean square. From the LILF, a potential conservatism produced by the derivative of the membership function is eliminated to increase the relaxation of sufficient conditions. Furthermore, those conditions are transferred into linear matrix inequality (LMI) form via projection lemma. According to the convex optimization algorithm, the feasible solutions are directly obtained to establish the static output fuzzy controller. Finally, a numerical example is applied to demonstrate the effectiveness and usefulness of the proposed design method.
Highlights
Some potential conservatisms for the static output feedback controller design method are caused by separating the variables to convert the sufficient conditions into linear matrix inequalities (LMIs)
Thispaper paperaddressed addressedthe thestatic static output control problem of nonlinear stochastic tems through application of the fuzzy model and
Based on the parallel distributed compensation (PDC) concept, concept, the output controller constructed withmeasured measured states to to keep the relaxation the output controller was was constructed with states keep the relaxation of of multiple matrices and, to avoid the derivative of the membership function, the line-integral Lyapunov function (LILF)
Summary
Some potential conservatisms for the static output feedback controller design method are caused by separating the variables to convert the sufficient conditions into linear matrix inequalities (LMIs). To propose the static output controller design method, some equalities are required [18] such that the derived conditions belong to LMI problems. Based on the Itô formula, some static output feedback controller design methods have been proposed by [28,29,30] so that the stability of nonlinear stochastic systems is guaranteed in the mean square. The relaxed output feedback controller design methods for polynomial stochastic systems [32] were proposed via applying the parameter-dependent Lyapunov function. This paper is structured as follows: In Section 2, the output feedback stability problem of nonlinear stochastic system is investigated via the T–S fuzzy system. I represents the identity matrix with appropriate dimension, E{·} represents the expected value of ·, He{·} represents the [·] + [·] T , and ∗ represents the symmetric parts in the block matrix
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