Abstract
The issue ofH∞estimation for a class of Lipschitz nonlinear discrete-time systems with time delay and disturbance input is addressed. First, through integrating theH∞filtering performance index with the Lipschitz conditions of the nonlinearity, the design of robust estimator is formulated as a positive minimum problem of indefinite quadratic form. Then, by introducing the Krein space model and applying innovation analysis approach, the minimum of the indefinite quadratic form is obtained in terms of innovation sequence. Finally, through guaranteeing the positivity of the minimum, a sufficient condition for the existence of theH∞estimator is proposed and the estimator is derived in terms of Riccati-like difference equations. The proposed algorithm is proved to be effective by a numerical example.
Highlights
In control field, nonlinear estimation is considered to be an important task which is of great challenge, and it has been a very active area of research for decades 1–7
The H∞ estimation problem 2.3 and the Lipschitz conditions 2.2 are combined in an indefinite quadratic form, and the nonlinearities are assumed to be obtained by {y i }ki 0 at the time step k
It is proved in this subsection that the H∞ estimation problem can be reduced to a positive minimum problem of indefinite quadratic form, and the minimum can be obtained by using the Krein space-based approach
Summary
Nonlinear estimation is considered to be an important task which is of great challenge, and it has been a very active area of research for decades 1–7. In , the linear matrix inequality- LMI- based fullorder and reduced-order robust H∞ observers are proposed for a class of Lipschitz nonlinear discrete-time systems with time delay. In , by guaranteeing the asymptotic stability of the error dynamics, the robust observer is presented for a class of uncertain discrete-time Lipschitz nonlinear state delayed systems; In , based on the sliding mode techniques, a discontinuous observer is designed for a class of Lipschitz nonlinear systems with uncertainty. The major contribution of this paper can be summarized as follows: i it extends the Krein space linear estimation methodology 26 to the state estimation of the time-delay Lipschitz nonlinear systems and ii it develops a recursive Kalman-like robust estimator for time-delay Lipschitz nonlinear systems without state augmentation. < ∞; the superscripts “−1” and “T ” stand for the inverse and transpose of a matrix, resp.; I is the identity matrix with appropriate dimensions; For a real matrix, P > 0 P < 0, resp. means that P is symmetric and positive negative, resp. definite; ∗, ∗ denotes the inner product in the Krein space; diag{· · · } denotes a block-diagonal matrix; L{· · ·} denotes the linear space spanned by sequence {· · ·}
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