POLYNOMIAL STATIC OUTPUT FEEDBACK H ∞ CONTROL FOR CONTINUOUS-TIME LINEAR SYSTEMS VIA DESCRIPTOR APPROACH

International audienceThis paper deals with the problem of the robust static output feedback H ∞ control (SOFC) for continuous linear systems with polytopic uncertainties. The controller has been gotten by the use of descriptor redundancy. Under this approach a sufficient condition is provided for the existence of a solution to the problem. Thus, the advantage of this method is to obtain more free matrices in the design condition, also the polynomial approach helps to have a less conservative result. In the end, the performance of the method is shown by several examples

Robust H-2 static output feedback design starting from a parameter-dependent state feedback controller for time-invariant discrete-time polytopic systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)This paper investigates the problem of computing robust H-2 static output feedback controllers for discrete-time uncertain linear systems with time-invariant parameters lying in polytopic domains. A two stages design procedure based on linear matrix inequalities is proposed as the main contribution. First, a parameter-dependent state feedback controller is synthesized and the resulting gains are used as an input condition for the second stage, which designs the desired robust static output feedback controller with an H-2 guaranteed cost. The conditions are based on parameter-dependent Lyapunov functions and, differently from most of existing approaches, can also cope with uncertainties in the output control matrix. Numerical examples, including a mass spring system, illustrate the advantages of the proposed procedure when compared with other methods available in the literature. Copyright (C) 2009 John Wiley & Sons, Ltd.321113Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Robust Constrained Model Predictive Control using Linear Matrix Inequalities

The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a state-feedback control law which minimizes a "worst-case" infinite horizon objective function, subject to constraints on the control input and plant output. Using standard techniques, the problem of minimizing an upper bound on the "worst-case" objective function, subject to input and output constraints, is reduced to a convex optimization involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon state-feedback control design robustly stabilizes the set of uncertain plants under consideration. Several extensions, such as application to systems with time-delays and problems involving constant set-point tracking, trajectory tracking and disturbance rejection, which follow naturally from our formulation, are discussed. The controller design procedure is illustrated with two examples. Finally, conclusions are presented

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

ROBUST STATIC OUTPUT FEEDBACK FOR DISCRETE-TIME SYSTEMS - LMI APPROACH

Two novel linear matrix inequality (LMI) based procedures to receive a stabilizing robust output feedback gain are presented, one of them being a modification of previous results of Oliveira et al., [5]. The proposed robust control law stabilizes the respective uncertain discrete-time system described by a polytopic model with guaranteed cost. The obtained results are compared with other LMI results from literature and illustrated on an example