Nonlinear Dynamics

, Volume 92, Issue 2, pp 415–427 | Cite as

Observer-based quantized sliding mode \({\varvec{\mathcal {H}}}_{\varvec{\infty }}\) control of Markov jump systems

Original Paper


An adjustable quantized approach is adopted to treat the \(\mathcal {H}_{\infty }\) sliding mode control of Markov jump systems with general transition probabilities. To solve this problem, an integral sliding mode surface is constructed by an observer with the quantized output measurement and a new bound is developed to bridge the relationship between system output and its quantization. Nonlinearities incurred by controller synthesis and general transition probabilities are handled by separation strategies. With the help of these measurements, linear matrix inequalities-based conditions are established to ensure the stochastic stability of the sliding motion and meet the required \(\mathcal {H}_{\infty }\) performance level. An example of single-link robot arm system is simulated at last to demonstrate the validity.


Markov jump systems Sliding mode Quantization \(\mathcal {H}_{\infty }\) control 



This work was supported by Basic Science Research Programs through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. NRF-2017R1A2B2004671), the National Natural Science Foundation of China under Grants (61403189, 61773200), the peak of six talents in Jiangsu Province under Grant 2015XXRJ-011, the China Postdoctoral Science Foundation under Grant 2015M570397, the Doctoral Foundation of Ministry of Education of China under Grant 20133221120012, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130949.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest to this work.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Electrical Engineering and Control ScienceNanjing Technology UniversityNanjingChina
  2. 2.Yeungnam UniversityKyongsanRepublic of Korea

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