Robust ℋ︁₂ static output feedback design starting from a parameter‐dependent state feedback controller for time‐invariant discrete‐time polytopic systems

Abstract

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.

Controle PID para sistemas lineares incertos de ordem arbitrária utilizando LMIs

“…A próxima técnica de projetoé conhecida na literatura como método dos dois estágios (Peaucelle and Arzelier, 2001;Arzelier et al, 2003;Moreira et al, 2011;Agulhari et al, 2012). Inicialmente projeta-se um controlador por realimentação de estados para o sistema (6) (note que nãó e necessário aplicar a transformação de similaridade na matriz C(α)).…”

Static and dynamic output feedback stabilisation of descriptor fractional order systems

“…Various ways of stabilisation controller design have been developed, among which a successful approach is the linear matrix inequality (LMI) method. On the basis of LMI, structured Lyapunov matrix method [30], two‐step method [31], iterative algorithm [32–35], the method of singular value decomposition (SVD) of matrices [36–41] have been advanced. In [38], the method of SVD of matrices is used to deal with the non‐linear problems caused by observer‐based robust control for FOS with order .…”

Mode-Independent <inline-formula> <tex-math notation="LaTeX">${\cal H}_{2}$ </tex-math> </inline-formula>-Control of a DC Motor Modeled as a Markov Jump Linear System

“…The method is inspired by the two-step design procedure developed in the context of deterministic systems for output feedback control in [13], [14], [15], that in [16], [17] have been extended to incorporate polynomially parameter-dependent matrices. In this paper, the method is adapted to cope with MJLS control design as follows: first determine a mode-dependent stabilizing gain; then use this gain as an input parameter for an LMI based procedure (called second stage) that, if feasible, provides a mode-independent stabilizing gain associated to an H 2 guaranteed cost.…”