Periodically Time-Varying ${\cal H}_{\infty}$ Memory Filter Design for Discrete-Time LTI Systems With Polytopic Uncertainty

A novel two-stage strategy for robust H∞ filter design of uncertain discrete-time systems

“…For example, on one hand, [25,26] suggested that the filter whose order is greater than that of plant can bring more degrees of freedom. On the other hand, utilizing the information built via summing filter's states over several samples from the past to the present, [27,28] proposed memory filter design procedures to obtain better filtering performances. Fourthly, to compensate the structural constraint of auxiliary matrix variable, scalar parameter idea was given in [23] and widely extended afterwards such as in [8,29].…”

“…Recently, relying on Finsler lemma, [22] derived more general extended filter design conditions that can contain the conditions from [8,23] as particular cases. Most recently, less conservative robust H ∞ filter design procedures were proposed in [27,28] where memory-based filter schemes were provided via exploiting the past filter states (the past measurements) to compute the current estimation. Note that, the filter design conditions in [8,22,23,27] have a common conservatism, which is the variable structural constraint in linearization of analysis condition.…”

LMI conditions for local stability and stabilization of continuous-time T-S fuzzy systems

“…Amongst the promising research topics, in this paper, we focus on the local stability approaches, which have turned out to be effective in improving the global approaches further [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]. Evaluation of the local stability is the problem of determining if there exists a neighborhood of the equilibrium point, called the domain of attraction (DA) [46], such that all trajectories of the system emanating from any initial point in the DA asymptotically converges to the equilibrium point.…”

LMI-based robust sampled-data stabilization of polytopic LTI systems: A truncated power series expansion approach

“…Nowadays, digital control systems are ubiquitous in real engineering applications, thanks to the rapid advancement of digital computer technology [1,[25][26][27][28][29][30][31][32][33][34][35]. Continuous-time (CT) systems controlled by a digital controller are referred to as sampled-data (SD) control systems, shown in Fig.…”