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H ∞ -filtering for a class of nonlinear time-delay systems
Abstract
In this paper, we consider the problem of robust H∞-filtering for a class of uncertain time-delay systems. This calss is nominally linear and has a known cone-bounded, state-dependent nonlinear term. The parametric uncertainty is real time-varying and the state-delay factor is unknown. We design a nonlinear estimator which renders the estimation error dynamics quadratically stable and provides a guaranteed H∞-performance of the filtering error for all admissible uncertainties and unknown state-delay.
... Thus, the class of dynamical systems with time-delay has attracted the attention of numerous investigators in the last two decades. Design of robust state estimators to different classes of continuous-time systems with parametric uncertainties and state-delay have been pursued in [9,14,15]. Despite the significant role of time-delays in discrete-time systems, a little attention has been paid to the class of uncertain discrete-time systems with delays. ...
... This paper contributes to the further development of robust state estimation techniques of classes of uncertain time-delay systems. The objective is to build upon the results of [14][15] for continuous-time systems. Specifically, the work reported here extends [14][15] to another dimension by considering the H ∞ -estimation of a class of discrete-time systems with real time-varying norm-bounded parametric uncertainties, unknown state-delay and Markovian jump parameters. ...
... The objective is to build upon the results of [14][15] for continuous-time systems. Specifically, the work reported here extends [14][15] to another dimension by considering the H ∞ -estimation of a class of discrete-time systems with real time-varying norm-bounded parametric uncertainties, unknown state-delay and Markovian jump parameters. On the other hand, our approach in this paper casts the results of [13,16,22] about H ∞ filtering for delay-free systems into the context of linear uncertain discrete-time systems with unknown-but-bounded statedelay. ...
In this paper, we examine the robust H∞ filtering problem for a class of linear, uncertain discrete delay systems with Markovian jump parameters. The uncertainties are time-varying and norm-bounded parametric uncertainties and the delay factor is arbitrary constant. We provide initially a robust stochastic stability result with a prescribed perfor-mance measure. Then we design a linear causal filter using algebraic inequality procedure which ensures a prescribed disturbance attenuation level from the disturbance signal to the filtering error.
The problem of delay-dependent robust dissipative filtering is investigated for a kind of Takagi-Sugeno (T-S) fuzzy descriptor system with immeasurable premise variables. By utilising the free-weighting matrix approach and combining them with the structural characteristics of the error system, we propose the solvable conditions of the dissipative filter that ensure an error system with immeasurable states is admissible and strictly dissipative. This implies that it is not necessary to assume that the error systems are regular and impulse-free prior to designing filters. The derived method can be applied broadly to nonlinear systems. Also, the solvable condition of the dissipative filter with measurable states is a special case of this study. We also elicit the design methods of the H∞ and passive filters, which could potentially reduce the cost and time spent on the filter design. Finally, we perform simulations to validate the derived methods for two kinds of nonlinear descriptor systems.
The problem of designing a resilient L2-Linfin filter for a class of linear uncertain state delay systems with uncertainties that belong to a convex-bounded polytopic domain is investigated. The objective is to derive tractable synthesis conditions for the resilient design of full-order and reduced-order filters such that a prescribed energy-to-peak disturbance-attenuation level is attained for all admissible uncertainties and gain perturbations. Both additive and multiplicative gain perturbations are considered. It is established that the filter design can be obtained from the solution of the convex optimisation problem over linear matrix inequalities. The design results are developed for both delay-independent and delay-dependent cases. In the latter case, two approaches are used: descriptor and extended Newton-Leibniz. Results on numerical simulations are presented to demonstrate the behaviour of the resilient filters.
We consider the robust H∞ filtering problem for a
general class of uncertain linear systems described by the so-called
integral quadratic constraints (IQCs). This problem is important in many
signal processing applications where noise, nonlinearity, quantization
errors, time delays, and unmodeled dynamics can be naturally described
by IQCs. The main contribution of this paper is to show that the robust
H∞ filtering problem can be solved using linear matrix inequality
(LMI) techniques, which are numerically efficient owing to recent
advances in convex optimization. The paper deals with both continuous
and discrete-time uncertain linear systems
A representation formula for all controllers that satisfy an L∞-type constraint is derived for time-varying systems. It is now known that a formula based on two indefinite algebraic Riccati equations may be found for time-invariant systems over an infinite time support (see [J.C. Doyle et al., IEEE Trans. Automat, Control, AC-34 (1989), pp. 831-847]; [K. Glover and J.C. Doyle, Systems Control Lett., 11 (1988), pp. 167-172]; [K. Glover et al., SIAM J. Control Optim., 29 (1991), pp. 283-324]; [M. Green et al, SIAM J. Control Optim., 28 (1990), pp. 1350-1371]; [D.J.N. Limebeer et al., in Proc. IEEE conf. on Decision and Control, Austin, TX, 1988]; [G. Tadmor, Math. Control Systems Signal Processing, 3 (1990), pp. 301-324]). In the time-varying case, two indefinite Riccati differential equations are required. A solution to the design problem exists if these equations have a solution on the optimization interval. The derivation of the representation formula illustrated in this paper makes explicit use of linear quadratic differential game theory and extends the work in [J.C. Doyle et al., IEEE Trans. Automat. Control, AC-34 (1989), pp. 831-847] and [G. Tadmor, Math. Control Systems Signal Processing, 3 (1990), pp. 301-324]. The game theoretic approach is particularly simple, in that the background mathematics required for the sufficient conditions is little more than standard arguments based on 'completing the square.'
Summarized are research accomplishments in the 12 month period Nov. 1, 1985 to Oct. 31, 1986. Significant advances have been made in nonlinear filtering based on robust estimation, on nonparametric detection, and on a new noise model for signal-dependent and multiplicative noise. Reference is made to 11 publications.
This paper investigates the problem of H∞ filtering for a class of uncertain continuous-time nonlinear systems with real time-varying parameter uncertainty and unknown initial state. We develop an infinite horizon H∞ filtering methodology which provides both robust stability and a guaranteed H∞ performance for the filtering error irrespective of the parameter uncertainty.
This paper deals with the robust minimum variance filtering problem for linear systems subject to norm-bounded parameter uncertainty in both the state and the output matrices of the state-space model. The problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty. Two methods for designing robust filters are investigated. The first one deals with constant parameter uncertainty and focuses on the design of steady-state filters that yield an upper bound to the worst-case asymptotic error variance. This bound depends on an upper bound for the power spectrum density of a signal at a specific point in the system, and it can be made tighter if a tight bound on the latter power spectrum can be obtained. The second method allows for time-varying parameter uncertainty and for general time-varying systems and is more systematic. We develop filters with an optimized upper bound for the error variance for both finite and infinite horizon filtering problems
A state estimation design problem involving parametric plant
uncertainties is considered. An estimation error bound suggested by
multiplicative white-noise modeling is utilized for guaranteeing robust
estimation over a specified range of parameter uncertainties. Necessary
conditions that generalize the optimal projection equations for
reduced-order state estimation are used to characterize the estimator
that minimizes the error bound. The design equations thus effectively
serve as sufficient conditions for synthesizing robust estimators.
Additional features include the presence of a static estimation gain in
conjunction with the dynamic (Kalman) estimator to obtain a nonstrictly
proper estimator