Robust ℋ℞ filter design for polytopic linear discrete-time delay systems via LMIs and polynomial matrices (original) (raw)
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IET Control Theory & Applications, 2013
This paper presents new robust linear matrix inequality (LMI) conditions for robust H ∞ full order filter design of discrete-time linear systems affected by time-invariant uncertainty and a time-varying state delay. Thanks to the use of a larger number of slack variables, the proposed robust LMI conditions contain and generalize other results from the literature. LMI relaxations based on homogeneous polynomial matrices of arbitrary degree are used to determine the state space realization of the full order filter, that can also be implemented with delayed state terms whenever the timedelay is available in real time. As another contribution, an iterative LMI-based procedure involving the decision variables is proposed to improve the H ∞ filter performance. Numerical experiments illustrate the better performance of the proposed filter when compared to other approaches available in the literature. −d 2 Z 1 (α) − δ 2 Q 4 (α) − d 2 Z 2 (α)
Robust ℋ2 filter design for polytopic linear systems via LMIs and polynomial matrices
2010
This paper presents new linear matrix inequality conditions for full order robust H 2 filter design for continuous and discrete-time polytopic linear systems with time-invariant uncertainty. Thanks to the use of a larger number of slack variables, the proposed conditions are less conservative than the existing conditions in the literature, containing recently published results as particular cases. Examples illustrate the better performance of the proposed filters when compared to other approaches for robust filter design.
An input–output approach to H∞ reduced filter design for polytopic time-varying delay systems
International Journal of Systems Science, 2018
This paper discusses the problem of delay-dependent robust H ∞ filtering design for polytopic systems with a time-varying delay. A new model transformation is firstly applied by employing a three-term approximation for the delayed state, which leads to a smaller approximation error than the two-term approximation. Then, based on the scaled small-gain Theorem combined with an appropriate Lyapunov-Krasovskii Functional, the H ∞ performance analysis of the filtering error system is examined and then the H ∞ full-and reduced-order filters are designed in terms of linear matrix inequalities via a simple linearisation technique. Before the end, a sufficient condition is presented to solve the problem of H ∞ filtering design for a time-delay system without polytopic uncertainties. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods.
Robust stabilization of polytopic discrete-time systems with time-varying delay in the states
49th IEEE Conference on Decision and Control (CDC), 2010
Convex conditions, expressed as linear matrix inequalities (LMIs), for stability analysis and robust design of uncertain discrete-time systems with time-varying delay are presented in this paper. Delaydependent and delay-independent convex conditions are given. This paper is particularly devoted to the synthesis case where convex conditions are proposed to consider maximum allowed delay interval. It is also presented some relaxed LMIs that yield less conservative conditions at the expense of increasing the computational burden. Extensions to cope with decentralized control and output feedback control are discussed. Numerical examples, including real world motivated models, are presented to illustrate the effectiveness of the proposed approach. (V.J.S. Leite). constant delay. The problem of robust filtering for discrete-time uncertain systems with delayed states is considered in some papers. Delayed state systems with norm-bounded uncertainties are studied in and with polytopic uncertainties in . In the last case the delay is time-invariant. Recently, the problem of output feedback has attracted attention and can be cited as examples of on going research. In special, presents results for precisely known systems with time-varying delay including both static output feedback (SOF) and dynamic output feedback. The conditions, however, are presented as an interactive method that relax some matrix inequalities. In time-varying delay is assumed and a nonlinear algorithm is proposed to obtain a stabilizing controller. In [24] the results of [11] are extended, including polytopic uncertainties and constant Lyapunov-Krasovskii matrices. An interesting application can be found in the context of network control system: although most of the studies in the literature on this subject deal with continuous-time models, nowadays there are some approaches using discrete-time models with delayed states . See also for a robust adaptive sliding mode control scheme applied to discrete-time systems with time-varying delay in the state and subject to norm-bounded uncertainties. In the context of discrete-time-varying systems with time-varying delay in the state, see for convex approaches to the dynamic output feedback controller design problem.
Journal of the Franklin Institute, 2011
Convex conditions, expressed as linear matrix inequalities (LMIs), for stability analysis and robust design of uncertain discrete-time systems with time-varying delay are presented in this paper. Delaydependent and delay-independent convex conditions are given. This paper is particularly devoted to the synthesis case where convex conditions are proposed to consider maximum allowed delay interval. It is also presented some relaxed LMIs that yield less conservative conditions at the expense of increasing the computational burden. Extensions to cope with decentralized control and output feedback control are discussed. Numerical examples, including real world motivated models, are presented to illustrate the effectiveness of the proposed approach. (V.J.S. Leite). constant delay. The problem of robust filtering for discrete-time uncertain systems with delayed states is considered in some papers. Delayed state systems with norm-bounded uncertainties are studied in and with polytopic uncertainties in . In the last case the delay is time-invariant. Recently, the problem of output feedback has attracted attention and can be cited as examples of on going research. In special, presents results for precisely known systems with time-varying delay including both static output feedback (SOF) and dynamic output feedback. The conditions, however, are presented as an interactive method that relax some matrix inequalities. In time-varying delay is assumed and a nonlinear algorithm is proposed to obtain a stabilizing controller. In [24] the results of [11] are extended, including polytopic uncertainties and constant Lyapunov-Krasovskii matrices. An interesting application can be found in the context of network control system: although most of the studies in the literature on this subject deal with continuous-time models, nowadays there are some approaches using discrete-time models with delayed states . See also for a robust adaptive sliding mode control scheme applied to discrete-time systems with time-varying delay in the state and subject to norm-bounded uncertainties. In the context of discrete-time-varying systems with time-varying delay in the state, see for convex approaches to the dynamic output feedback controller design problem.
Delay-Dependent Robust H ∞ Filter Design for Uncertain Linear Systems with Time-Varying Delay
Circuits, Systems & Signal Processing, 2009
A new delay-dependent robust H ∞ filtering design for uncertain linear systems with time-varying delay is investigated. Two kinds of time-varying delays are considered. One is differentiable uniformly bounded with a bounded delay derivative; the other is continuous uniformly bounded. A full-order filter is designed which ensures the asymptotic stability of the filtering error system and a prescribed level of H ∞ performance for all possible parameters which reside in a given polytope. By constructing a new Lyapunov functional which contains a triple integral term, new delay-dependent conditions for the existence of the H ∞ filter are derived which are less conservative than the existing ones. The filter gain can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, two numerical examples are given to show the effectiveness and the advantages of the proposed method.
Robust H∞ filter design for uncertain linear systems with multiple time-varying state delays
IEEE Transactions on Signal Processing, 2001
The problem of robust H∞ filtering for continuous-time uncertain linear systems with multiple time-varying delays in the state variables is investigated. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. The aim is to design a stable linear filter assuring asymptotic stability and a prescribed H∞ performance level for the filtering error system, irrespective of the uncertainties and the time delays. Sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities, which can be efficiently solved by means of powerful convex programming tools with global convergence assured. An example illustrates the proposed methodology
Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach
Mathematical Problems in Engineering, 2008
Sufficient linear matrix inequality LMI conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions.