This paper addresses the design of state- or output-feedback H/sub /spl infin// controllers that satisfy additional constraints on the closed-loop pole location. Sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane. These conditions are expressed in terms of linear matrix inequalities (LMIs), and the authors' formulation is therefore numerically tractable via LMI optimization. In the state-feedback case, mixed H/sub 2//H/sub /spl infin// synthesis with regional pole placement is also discussed. Finally, the validity and applicability of this approach are illustrated by a benchmark example.

H/sub /spl infin// design with pole placement constraints: an LMI approach

Self-scheduled H ∞ control of linear parameter-varying systems: a design example

This paper proposes a new probabilistic solution framework for robust control analysis and synthesis problems that can be expressed in the form of minimization of a linear objective subject to convex constraints parameterized by uncertainty terms. This includes the wide class of NP-hard control problems representable by means of parameter-dependent linear matrix inequalities (LMIs). It is shown in this paper that by appropriate sampling of the constraints one obtains a standard convex optimization problem (the scenario problem) whose solution is approximately feasible for the original (usually infinite) set of constraints, i.e., the measure of the set of original constraints that are violated by the scenario solution rapidly decreases to zero as the number of samples is increased. We provide an explicit and efficient bound on the number of samples required to attain a-priori specified levels of probabilistic guarantee of robustness. A rich family of control problems which are in general hard to solve in a deterministically robust sense is therefore amenable to polynomial-time solution, if robustness is intended in the proposed risk-adjusted sense.

https://www.sheffield.ac.uk/polopoly_fs/1.60408!/file/campi_scenario-optimization.pdf

The scenario approach to robust control design

Discusses analysis and synthesis techniques for robust pole placement in linear matrix inequality (LMI) regions, a class of convex regions of the complex plane that embraces most practically useful stability regions. The focus is on linear systems with static uncertainty on the state matrix. For this class of uncertain systems, the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary LMI regions. The resulting tests for robust pole clustering are all numerically tractable because they involve solving linear matrix inequalities (LMIs) and cover both unstructured and parameter uncertainty. These analysis results are then applied to the synthesis of dynamic output-feedback controllers that robustly assign the closed-loop poles in a prescribed LMI region. With some conservatism, this problem is again tractable via LMI optimization. In addition, robust pole placement can be combined with other control objectives, such as H/sub 2/ or H/sub /spl infin// performance, to capture realistic sets of design specifications. Physically motivated examples demonstrate the effectiveness of this robust pole clustering technique.

Robust pole placement in LMI regions

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 ...

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

This note describes a new framework for the analysis and synthesis of control systems, which constitutes a genuine continuous-time extension of results that are only available in discrete time. In contrast to earlier results the proposed methods involve a specific transformation on the Lyapunov variables and a reciprocal variant of the projection lemma, in addition to the classical linearizing transformations on the controller data. For a wide range of problems including robust analysis and synthesis, multichannel H/sub 2/ stateand output-feedback syntheses, the approach leads to potentially less conservative linear matrix inequality (LMI) characterizations. This comes from the fact that the technical restriction of using a single Lyapunov function is to some extent ruled out in this new approach. Moreover, the approach offers new potentials for problems that cannot be handled using earlier techniques. An important instance is the eigenstructure assignment problem blended with Lyapunov-type constraints which is given a simple and tractable formulation.

Continuous-time analysis, eigenstructure assignment, and H/sub 2/ synthesis with enhanced linear matrix inequalities (LMI) characterizations

This paper presents a method for assigning the poles in a specified disk by state feedback for a linear discrete or continuous time uncertain system, the uncertainty being norm bounded. For this the "quadratic d stabilizability" concept which is the counterpart of quadratic stabilizability in the context of pole placement is defined and a necessary and sufficient condition for quadratic d stabilizability derived. This condition expressed as a parameter dependent discrete Riccati equation enables one to design the control gain matrix by solving iteratively a discrete Riccati equation. >

Pole assignment for uncertain systems in a specified disk by state feedback

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.

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

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.

J. Bernussou

Papers

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

Continuous-time analysis, eigenstructure assignment, and H/sub 2/ synthesis with enhanced linear matrix inequalities (LMI) characterizations

Pole assignment for uncertain systems in a specified disk by state feedback

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

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