Mohamed Yagoubi

Extended

This technical note presents a complete solution to the nonstandard H2 output feedback control problem for continuous descriptor systems where unstable and nonproper weighting functions are used. In such a problem, the desired controller has to satisfy two conditions simultaneously: (i) the closed-loop is admissible and has a minimum H2 norm, (ii) only the internal stability of a part of the closed-loop is sought. The condition of the existence of such a controller is deduced. An explicit characterization of the optimal solution is also formulated, based on two generalized algebraic Riccati equations (GAREs) and two generalized Sylvester equations. A numerical example is included to illustrate the validity of the proposed results.

{\rm H}_{2}

This article explores, based on projection lemma, dilated linear matrix inequality (LMI) characterisations for linear time-invariant singular systems. The deduced formulations cover not only the existing results reported in the literature, but also complete some missing LMI conditions. This article also lightens the mutual relations of these characterisations and clarifies the relation between the dilated LMIs for the conventional state-space systems and those for singular systems. The well-known results for the state-space setting reported in the literature can be reviewed as special cases.

Controller Synthesis for Continuous Descriptor Systems

The problem of Hinfin, state-feedback control synthesis for a subclass of rational LPV (linear varying parameter) systems is studied. It is shown first that rational LPV systems may be equivalently recast as an affine descriptor LPV system. Working on such realizations and under some simplifying assumptions, sufficient conditions for stability and Hinfin, performance are proposed in terms of LMI (linear matrix inequalities). Based on these conditions, a LMI problem is formulated in order to design constant or affine (in the varying parameters) Hinfin state-feedback. The effectiveness of the controllers so obtained is illustrated through academic examples

Dilated LMI characterisations for linear time-invariant singular systems

This paper investigates the extended stabilization control problem for continuous-time descriptor systems (also refereed to as singular systems, implicit systems or generalized state-space systems) where unstable and nonproper weighting filters are used. In such nonstandard problem, the desired controller, called the extended stabilizing controller, has to satisfy two conditions simultaneously: (i) the closed-loop is admissible; (ii) only the internal stability of a part of the closed-loop is required. In terms of two generalized Sylvester-type equations, necessary and sufficient conditions for the existence of an observer-based extended stabilizing controller are given. Moreover, a parametrization of the class of extended stabilizing controllers is formulated.

About Gain Scheduled State Feedback Controllers for Rational LPV Systems

This paper proposes dilated LMI characterizations of admissibility, D-admissibility, H¿ and H2 norms for continuous-time descriptor systems. These dilated LMIs achieve less conservative results when dealing with robust admissibility/performance analysis of affine parameter-dependent descriptor systems. Furthermore, based on these conditions, the paper presents an iterative design procedure for multiobjective state feedback control of parameter dependent descriptor systems. The main idea underlying the proposed method is to linearize the products of controller parameter K and the auxiliary variable G by assigning a part of G. When initializing the proposed algorithm, the assignment takes into account an explicit characterization of G. The effectiveness of the proposed conditions and design method is shown through some numerical examples.

Parametrization of extended stabilizing controllers for continuous-time descriptor systems

This paper addresses the design of H2 gain scheduled observer based controllers for rational linear parameter varying systems (LPV). Such systems are equivalently recast as affine descriptor LPV systems. The stability of the closed loop is proved and the H2 performance is ensured thanks to a Youla parameter optimization. A numerical example is presented to illustrate the efficiency of the method.

Multiobjective controller synthesis for parameter dependent descriptor systems via dilated LMI characterizations

This paper provides new LMI-based conditions for the design of H2 gain scheduled controllers for rational linear parameter varying systems (LPV). Such systems are equivalently recast as affine descriptor LPV systems. Based on this, new sufficient LMI-based conditions for H2 performance analysis are proposed. These conditions can be turned to a finite set of LMIs and allow the use of parameter-dependent Lyapunov functions. Accordingly, new LMI conditions for the H2 gain scheduled controller synthesis problem are given. A numerical example highlights the effectiveness of the proposed conditions.

H 2 gain scheduled observer based controllers for rational LPV systems

Abstract This paper addresses the design of gain scheduled observer-based controllers for rational linear parameter varying systems (LPV). Such systems are equivalently recast as affine descriptor LPV systems. Based on this new realization a descriptor observer-based controller is designed by means of some new sufficient conditions given as LMIs. The stability of the descriptor closed-loop system is proved. A state space rational controller, with an observer-based structure, is then derived. The stability of the obtained rational closed-loop is also proved. A numerical example is presented to illustrate the efficiency of the method.

H 2 gain scheduling control for rational LPV systems using the descriptor framework

This paper presents a complete solution to the problem of comprehensive admissibility for descriptor systems with unstable and nonproper weights. In such non-standard circumstances, it is hard to render the closed-loop system admissible due to the uncontrollable and unobservable weights. The necessary and sufficient condition is given and a specifically structured output feedback controller is conducted in terms of the dynamics of the weighs. It is shown that determining suitable controllers for a given descriptor system with the presence of unstable and nonproper weights requires solving an admissibility problem for an augmented system explicitly constructed in this paper. A numerical example is included to illustrate the current result.

Gain scheduled observer state feedback controller for rational LPV systems

Abstract The design of H ∞ reduced order controllers is known to be a non convex optimization problem for which no generic solution exists. In this paper, the use of Particle Swarm Optimization (PSO) for the computation of H ∞ static output feedbacks is investigated. Two approaches are tested. In a first part, a probabilistic-type PSO algorithm is defined for the computation of discrete sets of stabilizing static output feedback controllers. This method relies on a technique for random sample generation in a given domain. It is therefore used for computing a suboptimal H ∞ static output feedback solution. In a second part, the initial optimization problem is solved by PSO, the decision variables being the feedback gains. Results are compared with standard reduced order problem solvers using the COMPl e ib benchmark examples and appear to be much than satisfactory, proving the great potential of PSO techniques.