Robust stability analysis of linear continuous/discrete-time systems with output feedback controllers

State feedback stabilization of linear time-varying systems on time scales

“…Doing so reveals a rich mathematical structure which has great potential for new applications in diverse areas such as adaptive control [20], real-time communications networks [21], [22], dynamic programming [34], switched systems [30], stochastic models [5], population models [37], and economics [3], [4]. The focus of this paper is the study of linear state feedback controllers [28], [35] in this generalized setting and to compare and contrast these results with the standard continuous and uniform discrete scenarios.…”

Design of robust-optimal output feedback controllers for linear uncertain systems using LMI-based approach and genetic algorithm

“…Because the output feedback controller design is usually based on the nominal values of these system matrices, it is interesting to know whether the closed-loop system remains asymptotically stable in the presence of time-varying uncertain parameters. Applying such existing robust stability analysis results [36,18,31,15,7,3,23,4,8,12,33,10,25,21,1]; and references therein to solve this problem is not easy, in that, after output feedback, there will be coupled terms of parameters in the closed-loop system matrix because of the uncertain parameters in both input and output matrices [24,5]. 0020-0255/$ -see front matter Ó 2010 Elsevier Inc. All rights reserved.…”

“…Though we may regard these coupled terms as new independent parameters if we insist on using those existing robust stability analysis results, Su and Foung [24] and Tseng et al [26] have shown that a conservative analysis conclusion may be reached. Therefore, Su and Foung [24] and Tseng et al [26] investigated the robust stability problem of linear systems with constant output feedback in the presence of time-varying elemental (structured) parameter uncertainties by directly considering the coupled terms in the problem formulation.…”

“…Therefore, Su and Foung [24] and Tseng et al [26] investigated the robust stability problem of linear systems with constant output feedback in the presence of time-varying elemental (structured) parameter uncertainties by directly considering the coupled terms in the problem formulation. Su and Foung [24] used the Lyapunov method to analyze the robust stability of linear continuous-time systems with quadratically-coupled elemental uncertainties. Tseng et al [26] applied the structured singular value technique to solve the robust stability analysis problem of linear continuous-time systems with quadratically-coupled elemental uncertainties.…”

“…Here it should be noted that only the articles of Su and Foung [24], Tseng et al [26], and Chen and Chou [5] studied the robust stability of linear continuous-time systems with output feedback controllers and time-varying uncertain parameters by directly considering the coupled terms in the problem formulation. That is, the research on the stability robustness of linear continuous-time systems with output feedback controllers and time-varying uncertain parameters by directly considering the coupled terms in the problem formulation is considerably rare and almost embryonic.…”