J. Bernussou

Extended H 2 and H norm characterizations and controller parametrizations for discrete-time systems

This paper presents new synthesis procedures for discrete-time linear systems. It is based on a recently developed stability condition which contains as particular cases both the celebrated Lyapunov theorem for precisely known systems and the quadratic stability condition for systems with uncertain parameters. These new synthesis conditions have some nice properties: (a) they can be expressed in terms of LMI (linear matrix inequalities) and (b) the optimization variables associated with the controller parameters are independent of the symmetric matrix that defines a quadratic Lyapunov function used to test stability. This second feature is important for several reasons. First, structural constraints, as those appearing in the decentralized and static output-feedback control design, can be addressed less conservatively. Second, parameter dependent Lyapunov function can be considered with a very positive impact on the design of robust H 2 and H X control problems. Third, the design of controller with mixed objectives (also gain-scheduled controllers) can be addressed without employing a unique Lyapunov matrix to test all objectives (scheduled operation points). The theory is illustrated by several numerical examples.

Robust Filtering of Discrete-Time Linear Systems with Parameter Dependent Lyapunov Functions

Robust filtering of linear time-invariant discrete-time uncertain systems is investigated through a new parameter dependent Lyapunov matrix procedure. Its main interest relies on the fact that the Lyapunov matrix used in stability checking does not appear in any multiplicative term with the uncertain matrices of the dynamic model. We show how to use such an approach to determine high performance H2 robust filters by solving a linear problem constrained by linear matrix inequalities (LMIs). The results encompass the previous works in the quadratic Lyapunov setting. Numerical examples illustrate the theoretical results.

An LMI optimization approach to multiobjective controller design for discrete-time systems

In this paper we investigate the design of multiobjective controllers for linear discrete-time systems. We show that, as for the H/sub 2/ norm, it is possible to extend the linear matrix inequality (LMI) characterization of the H/sub /spl infin// norm condition so that it no longer exhibits the product of the Lyapunov matrix and the system dynamic matrices. Then we develop a parametrization for state-feedback and output-feedback linear controllers which linearizes these extended H/sub 2/ and H/sub /spl infin// norm conditions for synthesis. These parametrizations are applied to the design of controllers with multiobjective constraints. A numerical example illustrates the results and provide a comparison with some of the existing methods.

H/sub 2/-norm optimization with constrained dynamic output feedback controllers: decentralized and reliable control

This paper addresses some open problems in the area of dynamic output feedback control design. The first one is the structurally constrained decentralized control problem, and the second is related to robust and reliable control. A necessary and sufficient condition for decentralized and quadratic stabilizability is given and used to provide a solution to the H/sub 2/-norm optimization problem. A numerical cross decomposition algorithm is developed and satisfactorily applied to find the solution of some illustrative examples. A comprehensive benchmark validates the results.

Design of dynamic output feedback decentralized controllers via a separation procedure

This paper investigates the well-known separation properties that hold in the design of unconstrained output feedback controllers and tries to generalize them to cope with the design of structurally constrained decentralized controls. This problem, which until now has been open, presents additional constraints which destroy the useful properties that lead to separation. Necessary and sufficient conditions for decentralized stability and H2 norm minimization are given, providing a framework in which a suitable ad hoc separation procedure is developed. A numerical algorithm based on crossdecomposition is presented and applied in two situations: first, when separation fails to provide a feasible solution; and then, to improve the obtained controller. An example and a comprehensive benchmark illustrate and validate the method.

Pole assignment of linear uncertain systems in a sector via a Lyapunov-type approach

The problem of designing robust control laws, in performance and in stability, for uncertain linear systems is considered. Performances are taken into account using root clustering of the closed-loop dynamic matrix in a sector of the complex plane. A synthesis procedure, based on a sufficient condition for quadratic stabilization and root clustering, such as stabilizability, is given, using an auxiliary convex problem. The results are illustrated by a significant example from the literature. >

Output feedback disk pole assignment for systems with positive real uncertainty

In this paper, the problem of pole assignment in a disk by output feedback for continuous or discrete-time uncertain systems is addressed. A necessary and sufficient condition for quadratic d stabilizability by output feedback is presented. This condition is expressed in terms of two parameter-dependent Riccati equations whose solutions satisfy two extra conditions. An output d stabilization algorithm is derived and a controller formula given. Some related problems are also discussed.

Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions

Robust filtering of linear time-invariant discrete-time uncertain systems is investigated through a new parameter dependent Lyapunov matrix procedure. Its main interest relies on the fact that the Lyapunov matrix used in stability checking does not appear in any multiplicative term with the uncertain matrices of the dynamic model. We show how to use such an approach to determine high performance H/sub 2/ robust filters by solving a linear problem constrained by linear matrix inequalities (LMI). The results encompass the previous works in the quadratic Lyapunov setting. Numerical examples illustrate the theoretical results.

An Analytical Formulation for Grade of Service Determination in Telephone Networks

The paper provides a simple method for point-to-point blocking estimation in telephone networks. A one-moment model is developed which incorporates the definition of fictitious offered traffic that enables one to take into account the deviation of smooth and peaked traffics from the Poisson. Numerical results illustrate the accuracy of the method.

An LMI Solution for Disk Pole Location with H2 Guaranteed Cost

In this paper, the problem of robust pole assignment in a disk with an H 2 guaranteed cost design is addressed. The uncertain systems considered are of norm bounded type and continuous as well as discrete time. The set of gains which assigns the closed-loop poles in a disk is characterised through a Linear Matrix Inequality (LMI). A way for selecting a gain in this set, which minimises an upper H 2 norm bound on the transfer matrix between a perturbation and a controlled output, is presented. It consists in solving a convex optimisation problem with a linear criterion and an L M I as a constraint.