Abstract
This paper is concerned with the stability of linear systems under time-varying sampling. First, the closed-loop sampled-data system under study is represented by a discrete-time system using a non-standard discretization method. Second, by introducing a new sampled-date-based integral inequality, the sufficient condition on stability is formulated by using a simple Lyapunov function. The stability criterion has lower computational complexity, while having less conservatism compared with those obtained by a classical input delay approach. Third, when the system is subject to parameter uncertainties, a robust stability criterion is derived for uncertain systems under time-varying sampling. Finally, three examples are given to show the effectiveness of the proposed method.
Highlights
Sampled-data systems have been widely applied in digital control systems and networked control systems [1,2,3,4,5]
This paper focuses on the stability of sampled-data systems under time-varying sampling
We refer to the discretization technique used in (8) as a non-standard discretization method
Summary
Sampled-data systems have been widely applied in digital control systems and networked control systems [1,2,3,4,5]. More and more attention has been focused on the stability analysis and synthesis of sampled-data systems [6,7,8,9,10,11,12,13,14]. The sampled-data systems are often those including continuous-time state and discrete-time control, simultaneously [15]. The following sampled-data control law is assumed by a zero-order holder for the system (1): u(t) = Kx (tk ), t ∈ [tk , tk+1 ) (2). Where K is the given controller gain of (2) and tk are the sampling instants satisfying 0 = t0 < t1
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