FIR-type state-feedback control law for discrete-time LTI systems with polytopic uncertainties

Linear matrix inequality‐based solution for memory static output‐feedback control of discrete‐time linear systems affected by time‐varying parameters

“…Even in the case of state‐feedback (), the structure of matrix in (3) poses a technical difficulty in the sense of deriving convex synthesis condition for the gains . In the literature of memory control, the usual technique to derive LMIs is constrained slack variables, which is a source of conservativeness 28‐31,33,34 . As presented next, this article proposes a strategy that does not resort to constrained slack variables to construct the control gains in terms of change of variables, such that the gains appear explicitly in the optimization procedure.…”

“…Although there are several works dealing with the design of memory filters and control laws, this article aims to contribute to memory control for LPV systems through a static output‐feedback control law, providing a more general stabilization method. Differently from the current mainstream of the control design strategies, where potential sources of conservativeness, such as constrained (in terms of structure and parameter‐dependency) optimization variables and matrices of the system, are the standard techniques employed to provide synthesis conditions in terms of LMIs, 28‐31,33,34 the proposed approach diverges significantly. Inspired by the strategy in Reference 36, the synthesis conditions are formulated such that the Lyapunov matrix and the control gains appear affinely.…”

“…In the last decade, past information (states or outputs) feedback gained a renewed interest, even for systems not affected by time‐delays. As a matter of fact, the artificial enrichment of the system dynamics has been proved to be a useful technique in the presence of unknown or time‐varying parameters, being used in filtering 23‐26 and control 27‐31 of uncertain systems and control of periodic systems 5,32‐35 . Basically, the Lyapunov stability theory is applied to an augmented system where the number of past information, a designer's choice, has been included.…”

Contributions to filter and control desing for LPV systems using LMIs

“…Seeking to improve performance in robust control and filtering design problems, one among many strategies in the literature is the artificial enrichment of the system dynamics by introducing past values of the states or outputs in the control law or in the dynamics of the filter. This technique has been used in filtering and control of time-invariant uncertain systems (LEE et al, 2009;LEE et al, 2014;LEE et al, 2015;FREZZATTO et al, 2015;LEE et al, 2015;LEE et al, 2016;ROMÃO et al, 2017;FREZZATTO et al, 2018;FREZZATTO et al, 2019). Basically applying the Lyapunov stability theory to an augmented system where the past information (states or outputs) is considered.…”