Abstract
This paper considers the reduced-order H ∞ filtering problem for singular Markovian jump systems (SMJSs) with incomplete transition rates (ITRs) by using augmented system method. The considered conditions in this paper are necessary and sufficient (NS), whereas the existing conditions are mainly sufficient. To be concrete, by extracting system matrices in the considered system from augmented system, NS condition for the existence of the full-order H ∞ filtering is provided in terms of linear matrix inequalities (LMIs). However, it is hard to extend the condition to the existence of the reduced-order H ∞ filtering. Thus, by fixing augmented system matrices, NS condition for the existence of the reduced-order one is presented to guarantee the desired filtering error system to be stochastically admissible with H ∞ performance level. Furthermore, there are neither complicated matrix transformation nor equality/rank constraints in this paper. One numerical and one practical examples are illustrated to demonstrate the effectiveness of the achieved results.
Highlights
Singular systems, referred to descriptor systems, implicit systems and generalized state-space systems [1], [2], which are formed by a set of coupled algebraic and differential equations
The reduced-order H∞ filtering problem is considered for singular MJSs (SMJSs) with incomplete transition rates (ITRs)
By using elimination method, the necessary and sufficient (NS) fullorder H∞ filtering is received for SMJSs with ITRs
Summary
Referred to descriptor systems, implicit systems and generalized state-space systems [1], [2], which are formed by a set of coupled algebraic and differential equations. It is difficult to implement the practical control systems to accurately estimate the TRs. study on the MJSs with ITRs receives the attention of researchers [10]. The reduced-order H∞ filtering problem is considered for SMJSs with ITRs. Note that the achieved H∞. By using elimination method, the necessary and sufficient (NS) fullorder H∞ filtering is received for SMJSs with ITRs. The filter matrices can be computed by a set of LMIs. similar with [19], the full-order NS conditions cannot be extended to the reduced-order ones due to some special matrix structure (such as i in [19]). Notation: Throughout this paper, Rn represents the n-dimensional Euclidean space; X T denotes the transpose of X ; ( , F, P) is a probability space with is the sample F is the algebra of subsets of sample space and P is the probability measure on F; ’*’ in LMIs represents the symmetric term of the matrix; X > 0(< 0) means X is a symmetric positive(negative) definite matrix; He[X ] means that X + X T ; λmin(X ) respects the minimum eigenvalue of X ; E(X ) denotes the mathematical expectation operator of X ; L2[0, ∞) refers to the space of square-integrable vector functions over [0, ∞); |X | denotes the Euclidean norm for vectors of X ; col[X , Y ] denotes [X T , Y T ]T ; diag{. . .} represent a block diagonal matrix
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