An LMI-Based Algorithm to Compute Robust Stabilizing Feedback Gains Directly as Optimization Variables

Control design of uncertain discrete‐time Lur'e systems with sector and slope bounded nonlinearities

“…Therefore, the results provided by Theorem 1 may be conservative, unless some golden rule could be used to define those input matrices. Instead, inspired by the method presented in Reference 23, the stability conditions can be relaxed in such a way that a given choice for $$$ \overline{Y} $$$ always guarantees the existence of a feasible solution and, therefore, an iterative algorithm can be constructed.…”

Robust Static Output Feedback Stabilization of Linear Systems Using Dissipativity Theory

“…The advantages of this approach are: i) it does not need to solve a state feedback control problem in a first stage, as it is common in the field, ii) in many cases it can be solved in a non-iterative manner, iii) no restriction on the output matrix is considered. Moreover, future work envisages the development of an iterative approach, to deal with the cases that we do not achieve ∆ 0, and also a detailed comparison with strategies already known in the literature as Felipe and Oliveira (2020); Agulhari et al (2012); Shu and Lam (2009); Dong and Yang (2007). Finally, future works will also consider parameter dependent Lyapunov functions in order to decrease conservatism of conditions.…”

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

“…To circumvent this problem, a relaxation is proposed. Unfortunately, the relaxation proposed in Reference 36 (for continuous‐time systems) is not useful because it only works for time‐invariant parameters, where the concept of eigenvalue is representative. A new relaxation is proposed in the sequence as another contribution of the article, capable to cope with LPV systems.…”

“…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. This fact provides a more general method since state‐ and output‐feedback and decentralized control can be handled indistinctly.…”