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The problem of finite-horizon H∞ outputfeedback tracking control for linear discrete time-varying systems with stochastic state-multiplicative parameter uncertainties is investigated. We consider three tracking patterns depending on the nature of the reference signal i.e : whether it is perfectly known in advance, measured on-line or previewed in a fixed time-interval ahead. The stochastic uncertainties...
Linear discrete-time systems with stochastic uncertainties in their state-space matrices are considered. The problems of finite-horizon state-feedback control and filtering are solved, taking into account possible cross-correlations between the uncertain parameters. In both problems, a cost function is defined which is the expected value of the standard H∞ performance index with respect to the uncertain...
In this paper we present some models of various enzymatic reaction systems amenable to analytic techniques of classical control theory. These models extend from simple and most abundant cases to more involved cases where (negative) feedback plays a major role at the level of a single enzyme reaction (including the so called ‘feed-back inhibition’). Using the above models we point at the specific feedback...
During the last decade, a considerable amount of attention has been payed to stability and control of continuous-time linear systems with delays (see e.g. [?], [?], [?], [?]-[?] and the references therein). Delay-independent and, less conservative, delay-dependent sufficient stability conditions in terms of Riccati or linear matrix inequalities (LMIs) have been derived by using Lyapunov-Krasovskii...
The problem of finding the H∞-norm of systems with a finite number of discrete delays and distributed delay is considered. Sufficient conditions for the system to possess an H∞-norm which is less or equal to a prescribed bound are obtained in terms of the Riccati partial differential equations (RPDE's). We show that the existence of the solution to the RPDE's is equivalent to the existence of the...
The problem of finite-horizon H∞ tracking for linear time-varying systems with stochastic parameter uncertainties is investigated. We consider three tracking patterns depending on the nature of the reference signal i.e : whether it is perfectly known in advance, measured on line or previewed in a fixed time-interval ahead. The stochastic uncertainties appear in both the dynamic and measurement matrices...
A new method is proposed for the solution of linear matrix inequalities over a finite horizon for linear discrete time varying systems with or without uncertainties. The method is used to solve a variety of problems beginning with the standard H∞ discrete-time bounded real lemma and extending through to robust H∞ general-filtering and output-feedback control design of uncertain systems. In the latter...
New delay-dependent bounded real criteria are derived for linear continuous-time retarded and neutral type systems. A sufficient condition for the system to possess a H∞-norm that is less than a prescribed level, is given in terms of a linear matrix inequality (LMI). A delay-dependent solution is obtained by using a descriptor model transformation of the system and by applying Park's inequality for...
An output-feedback model-following problem is solved, for linear time-delay systems with uncertainties, using robust simplified adaptive controllers. Sufficient conditions for closed-loop stability of the proposed simplified adaptive control scheme are given, in terms of Bilinear Matrix Inequalities. Stability is analyzed using the Lyapunov-Krasovskii functional method. The solutions are delay-dependent;...
The problem of robust H∞ control of uncertain linear switched system with dwell time is addressed. A Lyapunov function in a quadratic form, which is non-increasing at the switching instances, is assigned to each subsystem. This function is used to determine the stability and the L2-gain of the switched system, where a bounded real lemma (BRL) is derived that provides an upper-bound to the system L...
The problem of infinite-horizon H∞ state-feedback tracking for linear continuous time-invariant retarded systems with stochastic parameter uncertainties is investigated. We consider the case where the reference signal is previewed in a fixed time-interval ahead. The stochastic uncertainties appear in the dynamics matrices for both the retarded and the non retarded states of the system. The delayed...
Sufficient conditions are given for the stability of linear switched systems with dwell time and with polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, which is non-increasing at the switching instants is assigned to each subsystem. During the dwell time, this function varies piecewise linearly in time after switching occurs. It becomes time invariant afterwards. This function...
An output-feedback direct adaptive control problem is considered for a class of linear time delayed measurements systems with polytopic-type parameter uncertainties and disturbances. The objective is to make the system output follow the output of a system model and to attain guaranteed H∞ performance of the proposed adaptive control scheme. The time-delay is either constant (known) or time-varying...
In this paper a method for designing a reduced-order output feedback controller for a linear time-invariant retarded system with stochastic state-multiplicative Wiener-type noise, that achieves a minimum bound on the H∞ performance level, is introduced. The solution of the stochastic H∞ reduced-order output-feedback control problem is solved, for the stationary case, via the input-output approach...
A simple efficient method for addressing finite-horizon control problems is suggested for a class of linear time-varying systems by solving 'standard' (algebraic) linear matrix inequalities (LMIs). Considering the Lyapunov function xTP(t)x, a class of time-varying solutions for P(t) is derived without using differential inequalities. The core idea is to seek a P(t) which is linear in time, and to...
A linear parameter varying approach for designing a constant output feedback controller for a linear time-invariant retarded system with stochastic multiplicative Wiener-type noise, that achieves a minimum bound on the Hinfin performance level is introduced. The stochastic uncertainties appear in the dynamic matrices, which correspond to the delayed and non-delayed states of the system, and in the...
Robust output-feedback simplified adaptive control model following is considered for discrete-time systems with uncertainties and disturbances. Sufficient conditions for closed-loop stability, model following performance and prescribed H∞ disturbance attenuation level are introduced, under an almost-strictly-positive-realness requirement on the plant. A numerical example, taken from the field of flight...
Robust output-feedback simplified adaptive control model following with uncertainties and disturbances is considered. Sufficient conditions for closed-loop stability, model following performance and prescribed Hinfin disturbance attenuation level are introduced, under an almost-strictly-positive-realness requirement on the plant. A numerical example, taken from the field of flight control, demonstrates...
The problem of designing robust filter with guaranteed induced lscrinfin norm for the estimation of the state-vector of finite dimensional discrete-time linear systems is considered. The design process applies a lemma which was recently derived by the authors of this paper, characterizing the induced lscrinfin norm by Linear Matrix Inequalities. The results are applied to a tracking problem with uncertainty...
Linear, state delayed, norm bounded uncertain continuous-time systems with stochastic uncertainties in their state-space model are considered. The problems of both Hinfin robust state-feedback control and robust filtering are solved, for the stationary case, via an input-output approach by which the system is replaced by a nonretarded system with (additional) deterministic norm-bounded uncertainties...
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