Balanced truncation approach to model reduction of Markovian jump time-varying delay systems

Time‐weighted MR for switched LPV systems via balanced realisation

“…Remark 1: The multiple Lyapunov function method is used in this paper, which is less conservative than a common parameterindependent Lyapunov function method, especially in large parameter variation. Lemma 2 [24]: The switched LPV system (Σ) in (1) is minimal if and only if it is controllable and observable.…”

“…The gramians based method used to solve the MR problem based on balanced realisation can be applied to any system, stable or unstable and minimal or non-minimal, see [24,25]. The process for the MR is similar, and for brevity we only focus on stable and minimal systems.…”

Model reduction for discrete-time switched linear time-delayed systems with finite-frequency specifications

“…Su et al (2012) used the projection theorem to study the H N model reduction problem of continuous-time T-S fuzzy systems. The model approximation problem for the continuous-time Markov jump with time-varying delay and norm-bounded time-varying uncertainty was studied in Zhang et al (2015), where an balanced truncation method was expanded to solve this problem.…”

Performance limitation of networked control systems with networked delay and two-channel noises constraints

“…The stability analysis of sampling system by a new time-based discontinuous Lyapunov function was studied in Shao, Han, Zhao, and Zhang (2017). In NCSs, the network delay is time-varying or random (Gao, Jiang, & Pan, 2018;Su & Chesi, 2017;Tao, Wu, Su, Wu, & Zhang, 2018;Zhang, Wu, Shi, & Zhao, 2015). A new Lyapunov function and stability results are dependent on both the data packet dropouts and the time delay was proposed in Tao, Lu, Wu, and Wu (2017).…”