Abstract
This paper studies the problem of finite-time non-fragile extended dissipative control for the periodic piecewise time-varying systems. First, based on the time-varying Lyapunov matrix and the matrix polynomial condition, a sufficient condition of finite-time boundedness for periodic piecewise time-varying subsystem is derived, and the finite-time extended dissipative performance is then analyzed. Furthermore, considering two types of time-varying controller perturbations, the non-fragile controllers are developed, which can guarantee the finite-time boundedness of periodic piecewise time-varying systems and satisfy the extended dissipative performance at the same time. Finally, numerical examples demonstrate the effectiveness of the proposed methods.
Highlights
Periodic characteristics extensively exist in various fields, such as vibration system [1], hypersonic cruise vehicle [2], spacecraft magnetic attitude control [3]
The stability analysis and synthesis of discrete-time periodic systems can be conducted based on the FloquetLyapunov theory and the Lifting techniques
Periodic piecewise system consists of several subsystems and has the fixed switching sequence and dwell time of each subsystems
Summary
Periodic characteristics extensively exist in various fields, such as vibration system [1], hypersonic cruise vehicle [2], spacecraft magnetic attitude control [3]. For periodic piecewise polynomial time-varying systems, the stability analysis and H∞ control were studied in [13] and [14], respectively. The analysis of the finite-time extended dissipative performance for periodic piecewise time-varying system has not been reported so far. The non-fragile control strategies of periodic piecewise time-varying system were studied in [32], [33], but various performance indices are not taken into account. Motivated by the above works, the problem of finitetime extended dissipative control for periodic piecewise timevarying systems is studied in this paper. The main contributions of this paper are twofold: (1) The condition of finite-time extended dissipativity for periodic piecewise time-varying systems is proposed for the first time, which provides a choice for analyzing multiple performance of the system simultaneously. We use ∗ as an ellipsis for the terms introduced, D+(·) denotes the upper right Dini derivative
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