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Stability of a Class of Switched Positive Linear Time-Delay Systems

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... Here we consider arbitrary systems, which means that other parameters of the systems do not have to be positive. Continuous-time positive linear systems are also discussed by Zhao et al. (2013;2014) in the case of one time-delay and without delays, respectively. ...
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The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative
... The study of switched systems is a well established area of research in control theory, mainly motivated by their theoretical interest and technical advances in broad applications[1]. Many systems such as mechanical systems, electric power systems and control systems can be modeled as switched systems ([2,3]). ...
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In this paper, we prove the equivalence of weak attractivity, attractivity, global uniform asymptotic stability and exponencial stability of switched homogeneous systems whose switching signals verify a certain property P. In addition we show that these stability properties imply that the system stability is robust with respect to disturbances in a power-like sense, which comprises both, the exponential ISS and iISS.
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The problem of exponential L1 output tracking control for positive switched linear systems with time-varying delays is addressed in this paper. The exponential L1-gain performance index is introduced to study such a problem. By resorting to the average dwell time approach, and also by constructing an appropriate piecewise co-positive type Lyapunov–Krasovskii functional, a new delay-dependent exponential stability criterion is developed, and the exponential L1-gain performance is analyzed. Based on the results obtained, a state feedback controller is constructed such that the exponential L1 output tracking performance is satisfied. A numerical example is given to demonstrate the effectiveness of the proposed method.
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