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This paper investigates the H∞ Observer-Based Controller (H∞-OBC) for Disturbed Fractional-Order Systems with Time-Varying-Delay (D-FOS-TVD). First, the existence conditions for H∞-OBC are given. Then, based on the diffusive representation of the fractional-order derivative and the indirect Lyapunov approach proposed by [1], a new sufficient condition is obtained and presented as a convex optimization...
This study concerns the decentralized observer-based control for discrete time nonlinear interconnected system. The nonlinear interconnection between subsystem is uncertain and the only information about these uncertainties is that satisfy quadratic constraints. Sufficient conditions ensuring the synthesis of observer based feedback controller are established. The quadratic constraint is reformulated...
This paper investigates the synthesis of sufficient conditions for finite-time stability of nonlinear quadratic systems. For this purpose, we investigate the usefulness of combining the notion of annihilator with a version of Finsler's Lemma. The design conditions obtained by means of polynomial Lyapunov function are expressed in term of linear matrix inequalities.
This paper deals with observer-based controller design problem for discrete-time Linear Parameter Varying (LPV) systems with uncertain parameters. The proposed technique consists in designing an observer-based controller which stabilizes the LPV system, provided that the norm of the difference between the measured parameter and the real one does not exceed a tolerated maximum value. The particularity...
This note deals with observer design for Lipschitz nonlinear systems via LMI. A new LMI condition is proposed to solve the problem of H∞ circle criterion observer design. This enhanced LMI is less conservative than those proposed in the literature for the same class of systems by using the same methodology. Indeed, thanks to a new and judicious use of the Young's relation, additional degree of freedoms...
This paper deals with observer design for nonlinear Lipschitz systems via Linear Matrix Inequalities (LMIs). Based on some recent work on the LPV approach, less conservative results are provided. To obtain LMIs, algorithms are proposed to design, a priori, some suitable observer parameters that enhance the feasibility of the LMIs. Interesting guidelines and techniques are proposed to reduce the number...
In this work, existence and design of Robust Functional Observer (RFO) for Uncertain Fractional-Order Systems with Time-Varying-Delay (UFOS-TVD) are addressed. Usually, when the considered system is under the effect of structured uncertainties, this kind of problems, referred as ℓ2-gain rejection, aims at designing a RFO minimizing a given cost function subject to ℓ2-gain rejection constraint, which...
This note deals with H∞ observer design for Lipschitz nonlinear systems. Thanks to a new and judicious use of the Young's relation, new and less conservative LMI conditions are proposed to solve the problem of observer design. Two LMI design methods are provided. First, we propose a new enhanced LMI technique that allows to improve the standard LMI methods for Lipschitz systems. A second method is...
This paper deals with the problem H∞ of observer-based stabilization via LMI for nonlinear systems with Lipschitz nonlinearities. Thanks a new variant of the Young's inequality and a reformulation of the Lipschitz property, a new and less conservative LMI condition is proposed. This later contains more degrees of freedom and some existing results in the literature can be viewed as particular cases.
This paper investigates the synthesis of sufficient conditions for finite-time stabilization of nonlinear quadratic systems via a nonlinear static state controller. For this purpose, we consider polytopic domains rather than ellipsoidal domains, and we investigate the usefulness of combining the notion of annihilator with a version of Finsler's Lemma. The design conditions obtained are expressed in...
In this work, the stability and stabilization of fractional-order time-varying delay systems modeled in state space are considered. First, based on the indirect Lyapunov and Lyapunov-Krasovskii approaches, we provide a sufficient condition for the asymptotic stability for the fractional-order time-varying delay systems. Then, we give a sufficient condition guaranteeing the existence and the synthesis...
This paper investigates the synthesis of full order output dynamic controller for linear continuous system with norm-bounded disturbances. This controller ensures the finite time boundedness of the closed loop system and satisfies the ℋ∞ criterion. The design conditions obtained by means of Lyapunov functions are expressed in term of linear matrix inequalities.
In this work, the H∞ filtering problem for fractional-order time-varying-delay systems is investigated. In the absence of disturbances, the observer state x̂(t) should asymptotically converge to the actual state x(t). On the other case, when the system is subject to disturbances, the H∞ observer must minimize the effect of disturbances on the estimation error. On the basis of the indirect Lyapunov...
In this paper, sufficient conditions are given to stabilize a plant with a bistable compensator and a complete design to determine bistable compensators is presented. Then, sufficient existence conditions for stabilizing simultaneously three plants with the same compensator are developed and a simple design is provided. A generalization of this result is proposed for stabilizing simultaneously n plants.
In this paper we investigate the problem of the design of a controller based on H∞ functional filter, in a finite time stability context for linear continuous time-invariant systems affected by norm bounded disturbances. The finite-time H∞ boundedness criterion of the closed-loop system is investigated. The order of the controller is reduced since the designed functional filter has the same order...
For both continuous and discrete-time cases, this paper presents a simple solution to the robust H∞ unbiased functional reduced order filtering problem via LMI methods in the presence of norm-bounded time-varying uncertainties. Necessary and sufficient conditions for the existence and the stability of the unbiased filter are given in the nominal case; the filter differs from that of 11] (only nominal...
The problem under investigation is the design of an observer for non uniformly observable bilinear systems. The bilinear system can be separated into two subsystems: one is uniformly observable and the other is not. A high gain observer is designed for the “observable part” while an unbiased observer is synthesized for the “unobservable part”. The exponential stability of the observation error for...
The Moving horizon approach is extended to a discrete linear systems with unknown inputs. The state and the unknown inputs are estimated via the optimal state estimation of singular systems. A numerical example is presented to illustrate the performance of the proposed filter.
In this paper, the moving horizon recursive state estimator for linear singular systems is derived from the least squares estimation problem. It will be shown that this procedure yields the same state estimate as the Kalman filter for descriptor systems if the noise is Gaussian. A numerical example is presented to prove the performance of the proposed filter.
This paper deals with the ℋ∞ reduced order unbiased filtering problems for a nominal bilinear system. After solving the unbiasedness condition with an algebraic framework, an LPV approach is used to reduce the conservatism inherent to the boundeness of the inputs and the ℋ∞ filtering. Then the reduced order filtering solution is expressed in terms of LMI to verify at the vertices of a polytope.
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