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

Oliveira, Maurı́cio C. de; Geromel, J.C.; Bernussou, J.

doi:10.1080/00207170210140212

Cited by 677 publications

(470 citation statements)

References 17 publications

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“…This is just a sample of possible problems and many more can be considered, such as robust or state feedback synthesis (see e.g., [2]), linear parameter-varying (LPV) design (see, e.g., [5] for a formulation of the LPV synthesis problem in the form of a robust convex semidefinite program, and [24] for a randomized solution approach, alternative to the one proposed in this paper), LP-based robust pole assignment (see [32]), the various robust design problems based on parameter-dependent linear matrix inequalities presented in [1], as well as problems in the robust model predictive control setup. For discrete-time systems, the robust analysis and design criteria proposed in [21] and [22] are also directly suitable for the scenario technique. Also, problems of set-membership state reachability and filtering [14], [18] may be efficiently solved in a probabilistic sense by the proposed methodology.…”

Section: Other Problemsmentioning

confidence: 99%

The Scenario Approach to Robust Control Design

Calafiore

Campi

2006

IEEE Trans. Automat. Contr.

976

804

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Abstract-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.

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Section: Other Problemsmentioning

confidence: 99%

The Scenario Approach to Robust Control Design

Calafiore

Campi

2006

IEEE Trans. Automat. Contr.

976

804

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“…On the other hand, it is noted that the aforementioned research efforts have been focused on the use of a single quadratic Lyapunov function (de Oliveira et al 2002;Haddad and Bernstein 1995), which tends to yield more conservative conditions. More recently, there appeared a number of results on stability analysis and control synthesis of 1-D dynamic systems based on basis-dependent Lyapunov functions (Choi and Park 2003;Gao et al 2009;Guerra and Vermeiren 2004;Zhou et al 2007).…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

Chen

Lam

Gao

et al. 2011

Multidim Syst Sign Process

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This paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini-Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples.

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“…Similar to the regional pole placement case, the H 2 and H ∞ control problems have been the subject of recent research, e.g. [21,22].…”

Section: Introductionmentioning

confidence: 99%

“…The polytopic representation is one of the most used approaches for describing uncertainty or variability of the parameters in linear parameter-varying (LPV) systems. Looking at [2,5,19,7,21,8,12,13], it can be seen that a lot of effort has been put in developing techniques for regional pole placement and H 2 /H ∞ control of polytopic systems, taking advantage of some useful properties of LMIs that allow to assure that their satisfaction at some points, i.e. the vertices of the polytope, implies their satisfaction in all points inside the polytope.…”

Section: Introductionmentioning

confidence: 99%

Design of parameter-scheduled state-feedback controllers using shifting specifications

Rotondo

Nejjari

Puig

2015

Journal of the Franklin Institute

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In this paper, the problem of designing a parameter-scheduled state-feedback controller is investigated. The paper presents an extension of the classical regional pole placement, H 2 control and H ∞ control problems, so as to satisfy new specifications, that will be referred to as shifting pole placement control, shifting H 2 control and shifting H ∞ control, respectively. By introducing some parameters, or using the existing ones, the controller can be designed in such a way that different values of these parameters imply different regions where the closed-loop poles are situated, or different performances in the H 2 or H ∞ sense. The proposed approach is derived within the so-called Lyapunov shaping paradigm, where a single quadratic Lyapunov function is used for ensuring stability and desired performances in spite of arbitrary parameter time variation. The problem is analyzed in the continuous-time LPV case, even though the developed theory could be applied to LTI systems in cases when it is desired to vary the control system performances online. Results obtained in simulation demonstrate the effectiveness and the relevant features of the proposed approach.

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

Cited by 677 publications

References 17 publications

The Scenario Approach to Robust Control Design

The Scenario Approach to Robust Control Design

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

Design of parameter-scheduled state-feedback controllers using shifting specifications

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