Robust Stability of Periodic Systems with Memory: New Formulations, Analysis and Design Results

Periodically time-varying memory static output feedback stabilization of discrete-time LTI systems with polytopic uncertainties: An LMI approach

“…Inspired by the recently developed periodically time-varying memory state-feedback controller (PTVMSFC) [13]- [18], we suggest the following periodically time-varying memory static output feedback controller (PTVMSOFC) or simply L-periodic controller:…”

“…In the late 1990s, the so-called extended Schur complement and slack variable approaches were developed by the pioneering work [5], [6], which played a significant role in the subsequent development of the LMI-based robust analysis and control approaches [7]- [18]. Recently, a new paradigm emerged in the field of robust control of discrete-time LTI systems [13]- [18], where the so-called periodically timevarying memory state-feedback controller (PTVMSFC) was proposed and turned out to be effective in reducing the conservatism in the constant state-feedback approaches.…”

“…Motivated by the PTVMSFC approach [13]- [18], the result in this paper provides, through a systematic and compact fashion, a generalization of the PTVMSFC technique to * cope with robust static output feedback (SOF) stabilization problem for discrete-time LTI systems with polytopic uncertainties. The SOF design may be one of the active and open problems in control theory, and much work has been done on developing efficient methods to solve the problem [19]- [29], [31]- [39].…”

A convex optimization approach to adaptive stabilization of discrete‐time LTI systems with polytopic uncertainties

“…In the late 1990s, the so-called extended Schur complement and slack variable approaches were developed by the pioneering work [8,9], which played a significant role in the subsequent development of the LMI-based robust analysis and control approaches. More recently, an important advance on robust stabilization of discrete-time LTI systems was accomplished in [23,24], where the so-called periodically time-varying state-feedback controller was proposed and turned out to be effective in reducing the conservatism in the static state-feedback approaches.On the other hand, adaptive control technology [25-29] has a long history of interest in the control community [30][31][32][33] and has attracted considerable attention to date. One of the advantages of the adaptive control approach is the ability to adjust the controller so as to cope with complex, uncertain, and highly nonlinear nature of the plant especially in the absence of complete information on the system.…”

“…In the late 1990s, the so-called extended Schur complement and slack variable approaches were developed by the pioneering work [8,9], which played a significant role in the subsequent development of the LMI-based robust analysis and control approaches. More recently, an important advance on robust stabilization of discrete-time LTI systems was accomplished in [23,24], where the so-called periodically time-varying state-feedback controller was proposed and turned out to be effective in reducing the conservatism in the static state-feedback approaches.…”