Summary
In this paper, the L1 filtering problem is studied for continuous‐time switched positive linear systems (SPLSs) with a small delay existing in the switching of the filter and the subsystem. Unlike the existing literature concerned with asynchronous problems of SPLSs, the synchronous and asynchronous filters will be designed separately, which implies less conservative results. By introducing a class of clock‐dependent Lyapunov function (CDLF), which jumps down when the modes of the filter or the subsystem change and may increase or decrease during the asynchronous interval, clock‐dependent sufficient conditions characterizing a nonweighted L1‐gain performance of the filter error systems are established. Then, based on the L1 analysis results, a pair of error‐bounding filters are designed to estimate the outputs of SPLSs. The filter gains can be obtained by solving a set of linear programming. Finally, two numerical examples are presented to show the effectiveness and advantages of the results.
This article is mainly concerned with quantized stabilization for switched affine systems with the periodic event‐triggered mechanism. By considering the effect of the event‐triggered scheme, a mathematical model for a closed‐loop control system with quantization is constructed. Theorems for main results are developed to guarantee the practical stability of the desired equilibrium point by using Lyapunov stability theory and linear matrix inequality techniques. Based on the derived sufficient conditions in theorems, the state feedback gains together with a switching function are presented in an explicit form. At last, a numerical example is proposed to illustrate our approach.
In this paper, the stability problem of discrete-time switched nonlinear systems with all subsystems unstable is investigated. The nonlinear subsystems are represented by the Takagi-Sugeno (T-S) fuzzy models. By constructing a novel piecewise multiple Lyapunov function approach, an exponential stability condition of switched T-S fuzzy systems is first established with the bounded maximum average dwell time. A numerical example is finally provided to illustrate the effectiveness of the obtained theoretical results.INDEX TERMS Discrete-time switched nonlinear systems, Takagi-Sugeno (T-S) fuzzy models, bounded maximum average dwell time (BMADT), piecewise multiple Lyapunov function (PMLF).
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