Section 4 presents a numerical example to demonstrate the effectivity of the mentioned methodology. Some conclusions are drawn in Section 5. We use R n to denote the n-dimensional Euclidean space.

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I and 0 denote the identity and zero matrices with appropriate dimensions. The superscript T denotes the transpose for vectors or matrices.

The set S comprises the operation modes of the system. It is assumed that A f i is nonsingular. Then the filtering error system is. In this section we address the problems of admissibly finite-time stochastic stability analysis and the filter design of the discrete-time Markov Jump stochastic system.

A sufficient condition of the filter existence and the design technique is proposed in the following theorems. Theorem 2 The filtering error system 5 is FTSS with respect to c 1 , c 2 , P , N and the error signal satisfies 7 , if there exist positive definite. Moreover, the suitable filter parameters A f i , B f i , L f i in system 4 can be given by.

We now give a numerical example to illustrate the proposed approach. In this example, we choose the following coefficients for the discrete-time Markov Jump stochastic system in the form of 1 :. Thus the system is finite-time stochastic stable with respect to 0. Moreover, applying Theorem 2, we can obtain the corresponding filter parameters as follows:.

Stochastic Lyapunov function method is adopted to establish sufficient conditions for the FTSS of the filter error system. An example is given to demonstrate the validity of the proposed method. Journals by Subject. Journals by Title. Author s Aiqing Zhang.

## Markov Jump Linear Systems-Based Position Estimation for Lower Limb Exoskeletons

Sufficient conditions of filtering design for the system under consideration are developed and the corresponding filter parameters can be achieved in terms of linear matrix inequalities LMI. Finally, a numerical example is provided to illustrate the validity of the proposed method. Introduction Since Markov Jump systems is important class of stochastic dynamic systems, it has drawn a lot of attention.

We now summarize several needed results from the literature. The next two Lemmas will play a key role in what follows.

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Numerical Example We now give a numerical example to illustrate the proposed approach. Cite this paper Zhang, A. Journal of Applied Mathematics and Physics , 6 , Todorov , Marcelo D. Fragoso Published in Int. Control DOI: These operators appear in the study of mean square stability for this class of systems. View via Publisher. Save to Library.

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References Publications referenced by this paper. Fragoso , Ricardo Paulino Marques.