Delay-Dependent H∞ Control of Uncertain Discrete Delay Systems (original) (raw)
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International Journal of Robust and Nonlinear Control, 2008
This paper deals with delay-dependent H 1 control for discrete-time systems with time-varying delay. A new finite sum inequality is first established to derive a delay-dependent condition, under which the resulting closed-loop system via a state feedback is asymptotically stable with a prescribed H 1 noise attenuation level. Then, an iterative algorithm involving convex optimization is proposed to obtain a suboptimal H 1 controller. Finally, two numerical examples are given to show the effectiveness of the proposed method.
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.
Convex Robust H-Infinity Control Design to Discrete-Time Systems with Time-Varying Delay
2011
The H ∞ control of uncertain discrete-time systems with time varying delay affecting the state vector are investigated in this paper. The uncertainties are supposed polytopic and may affect all matrices of the system. Convex conditions expressed as linear matrix inequalities (LMIs) are proposed for the design of robust state feedback control gains that assures an H ∞ guaranteed cost between the measured output and the exogenous input. These conditions are delay-dependent and are obtained by using parameter dependent Lyapunov-Krasovskii (L-K) functions and slack matrix variables that decouple the matrices of the system from the L-K function ones, yielding less conservative conditions. Crossed terms are tightly over bounded by means of Jensen's inequality. An extension based on following-model control design is proposed. A numerical example is presented to illustrate the efficacy of the proposal.
H∞ Control of Distributed and Discrete Delay Systems via Discretized Lyapunov Functional
European Journal of Control, 2009
The discretized Lyapunov functional method is extended to linear systems with both, discrete and distributed delays, and to H1 control. The coefficients associated with the distributed delay are assumed to be piecewise constant. A new Bounded Real Lemma (BRL) is derived in terms of Linear Matrix Inequalities (LMIs) via descriptor approach. In three numerical examples considered for retarded type systems, the resulting values of H1-norm converge to the exact ones. The analysis results are applied to state-feedback H1 control of linear neutral systems with discrete and distributed delays, where the controller may be either instantaneous or may contain discrete or distributed delay terms. A numerical example illustrates the efficiency of the design method and the advantage of using distributed delay term in the feedback for H1 control of systems with state delay.
Stability and guaranteed cost control of uncertain discrete delay systems
International Journal of Control, 2005
Robust stability and the guaranteed cost control problem are considered for discrete-time systems with time-varying delays from given intervals. A new construction of Lyapunov-Krasovskii functionals (LKFs), which has been recently introduced in the continuous-time case, is applied. To a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the system with the perturbed delays and that vanish when the delay perturbations approach zero. The nominal LKF is chosen in the form of the descriptor type and is applied either to the original or to the augmented system. The delayindependent result is derived via the Razumikhin approach. Guaranteed cost state-feedback control is designed. The advantage of the new tests is demonstrated via illustrative examples.
Delay-dependent robust H∞ control of uncertain linear systems with lumped delays
2005
This paper develops a Linear Matrix Inequality (LMI) approach to the robust H∞ control problem of uncertain continuous-and discrete-time linear time-invariant systems with time-delay in the state vector and control input. The main results provide sufficient delay-dependent conditions for the control problem, where the explicit size of the time delay plays a crucial role for the closed-loop stability. The solutions that are found for the H∞ control problem are less conservative, when compared to other approaches.
A convex approach for robust state feedback control of discrete-time systems with state delay
2004
In this paper, uncertain discrete-time systems with state delay are investigated. The uncertainty is supposed to belong to a known convex polytope. Linear matrix inequality conditions are given for the robust stability of the system, encompassing quadratic stability based results. Then, convex conditions assuring the existence of a robust state feedback gain are derived, assuring the delay independent quadratic stability of the closed-loop system (thus allowing to deal with time-varying uncertain systems) or, in the time-invariant case, guaranteeing the robust stability irrespective of the value of the delay. Moreover, the feedback control law can also include a term depending on the delayed state which, if the value of the delay is known, can be used to improve the control design. Numerical examples illustrate the effectiveness of the proposed techniques.