2004
DOI: 10.1590/s0103-17592004000300004 View full text |Buy / Rent full text
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Abstract: This paper deals with the fuzzy-model-based control design for a class of Markovian jump nonlinear systems. A fuzzy system modeling is proposed to represent the dynamics of this class of systems. The structure of the fuzzy system is composed of two levels, a crisp level which describes the Markovian jumps and a fuzzy level which describes the system nonlinearities. A sufficient condition on the existence of a stochastically stabilizing controller using a Lyapunov function approach is presented. The fuzzy-model… Show more

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“…Hence (12) is equivalent to (11). Therefore, in the presence of unknown elements in the transition rates matrix, one can readily conclude that the system is stable if and only if (10) and (11) hold for ∈ and ∈ , respectively.…”
Section: Stability Analysis and Stabilizationmentioning
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“…Hence (12) is equivalent to (11). Therefore, in the presence of unknown elements in the transition rates matrix, one can readily conclude that the system is stable if and only if (10) and (11) hold for ∈ and ∈ , respectively.…”
Section: Stability Analysis and Stabilizationmentioning
“…By Schur complement, we can obtain that (26) is equivalent to (27). In a similar way, if ∈ , (18) and (19) can be worked out from (11). (10)-(11) will be satisfied in Theorem 1 such that the closed-loop system (8) is stochastically stable.…”
Section: Stability Analysis and Stabilizationmentioning
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“…In fact, it can be shown that T-S fuzzy systems are universal approximators [13]. Recently, a fuzzy-model-based control technique for a class of Markovian jump nonlinear system was introduced in [14] and [15]. In this approach, the class of systems is represented by a fuzzy system model with two levels of structure: A crisp level which describes the jumps of the Markov process and a fuzzy level which describes the system nonlinearities.…”
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“…In this paper, we include in the fuzzy control design the approximation error between the fuzzy model and the nonlinear system and the two-level structured fuzzy model as in [14][15]. Actually, the effect of the approximation error can deteriorate the stability and control performance of nonlinear control systems [16].…”
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