H∞ and H2 memory static output-feedback control design for uncertain discrete-time linear systems

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.…”

“…To perform at least one comparison with a technique capable to produce memory controllers, the database of systems is tested considering the parameters as time‐invariant. In this case the method from Frezzatto et al 31 (FOP) can be applied. The overall result of A1 is 99.8% with m = 2 and FOP gives 73.1% with m = 4 memories.…”

“…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.…”

Output feedback controller design for discrete LTI systems with polytopic uncertainty via direct searching of the design space

“…Although, some novel and valuable approaches are developed, this problem is still an open challenge [12]. It is mainly because, there is a lack of a suitable and acceptable approach that is able to solve this problem by a set of sufficient and necessary conditions [13,14]. Among various approaches in this area, the Lyapunov-based methods are the most widely popular and common approaches.…”