Mohamed Benhayoun

Stabilization of 2D saturated systems by state feedback control

The problem of stabilizability of the 2D continuous-time saturated systems under state-feedback control is solved in this paper. Two cases are considered: the first one, the control may saturate and limits may be attained. The second one, the control does not saturate and limits are avoided. Sufficient conditions of asymptotic stability are presented. The synthesis of the required controllers is given under LMIs form. Illustrative examples are treated.

Stabilization of Continuous-Time Fractional Positive Systems by Using a Lyapunov Function

The stabilization problem for continuous-time fractional linear systems with the additional condition of non negativity of the states is solved. The obtained results are based on a direct Lyapunov function. In particular, the synthesis of state-feedback controllers is obtained by giving conditions in terms of Linear Programs. The solution is also extended to stabilization by asymmetric bounded control. Illustrative examples are provided to show the usefulness of the results.

Delay-Dependent Stabilizability of 2D Delayed Continuous Systems with Saturating Control

This paper deals with the problem of stability and stabilization of 2D delayed continuous systems with saturation on the control. An improved delay-dependent stability condition taken from the recent literature is first extended to the case of 2D systems. Second, a delay-dependent stabilizability condition is deduced. The synthesis of stabilizing saturating state feedback controllers for such systems is then given. A set of allowed delays for both directions of the state is computed. All involved conditions are given under LMI formalism. Examples are worked to show the effectiveness of the approach.

Stabilization of positive constrained T–S fuzzy systems: Application to a Buck converter☆

Abstract This paper deals with the problem of constrained stability and tracking of Takagi–Sugeno (T–S) fuzzy positive systems. Linear programming (LP) is used to insert the constraints in the design phase while imposing positivity in closed-loop. The theoretical results are applied to the buck DC–DC converter which is widely used in the photovoltaic generators. Based on the simulation results success of the method is shown for this application.

System stabilization by unsymmetrical saturated state feedback control

This paper studies the problem of linear unsymmetrical constrained input systems. A new transformation for constrained input linear problem control is presented to deal with the asymmetry of the constraints. LMI form is selected by using the available results on symmetrical saturation. These results are obtained for the first time reducing considerably the conservatism of the results obtained with symmetrical saturations. A numerical example is given to illustrate the new results.

Robust stabilization of constrained uncertain continuous-time fractional positive systems

Abstract The robust stabilization problem is solved for uncertain fractional linear continuous-time systems having bounded asymmetric control, with additional condition of non-negativity of the states. The synthesis of state-feedback controllers is obtained by giving conditions in terms of Linear Programs. An illustrative example is provided to show the usefulness of the results.

Stabilization of Systems with Unsymmetrical Saturated Control: An LMI Approach

This paper deals with the regulator problem for linear continuous-time systems with asymmetric saturations on the control. The main contribution of this work is to extend the available results for symmetrical saturations, in term of LMIs, to systems with asymmetric saturations. Hence, LMIs formalism is obtained for the first time for asymmetrical saturation. New less conservative result on saturation is used. An example is presented to illustrate the obtained results.

Continuous-time fractional bounded positive systems

Necessary and sufficient condition for a positive fractional linear continuous-time system to have its pseudo state bounded in a given interval is presented. Some previous results about fractional positive systems are completed. Generalization of an expression for the exponential function is obtained for the Mittag-Leffler function. Finally, necessary and sufficient condition is obtained for fractional positive systems to have their pseudo state bounded. An illustrative example is provided to show the usefulness of the results.

Constrained Control and Rate or Increment: An LMI Approach

This chapter solves the problem of designing stabilizing regulators for linear system subject to input saturation or magnitude input constraints together with asymmetric constraints on its increment or rate. Reduced dimension LMIs developed on a reduced-order state space are given. Compared with previous approaches, the proposed technique is valid for asymmetric constraints on the increment or rate of the control, while the computing time is improved by solving reduced dimension LMI.

Regulator Problem for Singular Linear Systems with Constrained Control

This chapter solves the problem of controlling singular continuous-time systems with constraints on the control magnitude and its rate, by using state and derivative feedback (proportional-derivative controllers). Necessary and sufficient conditions for positive invariance are proposed. The synthesis of the controller is presented using two methods: an exact method based on non-symmetric Riccati equations and an approximate method based on the solution of equation \(XA+XBX=HX\). An example illustrates the feasibility of the proposed approach. As a particular case, the extension to non-singular systems is also presented.