Robust stability and stabilization of uncertain switched discrete-time systems (original) (raw)
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A convex approach is proposed to deal with switched discrete-time systems with time-varying delays. It uses a parameter dependent Lyapunov-Krasovskii functional that allows to assure the robust stability or the robust stabilization of a switched system for arbitrary switching functions. The analysis and the design conditions are formulated as simple feasibility tests of linear matrix inequalities (LMIs). The presented conditions encompass previous results found in the literature, yielding less conservative and convex design methods. The design conditions can take into account the rate of variation of delay and deal with decentralized control. A design example is presented to illustrate the efficacy of the proposed LMI conditions, including some time-simulations.
Stabilization of Continuous-time and Discrete-time Switched Systems : A Review *
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Stability problem for a class of linear continuous time and discrete time systems is well understood since long. This analysis has also been extended to switched linear systems with continuous and discrete descriptions. For such cases, arbitrary switching problem is addressed by constructing common quadratic and non-quadratic Lyapunov function. Moreover, keeping in view the invertible time delays in dynamical systems due to internal factors or external environment, study of switched systems with delays has become quite challenging. The present work, highlights the state of art review of switched systems and underlying methodologies to ensure stabilization of such system with individual systems having stable or unstable dynamics. Further, current status and future directions of possible scope and open challenges in this area are also highlighted for completeness.