Finite‐time annular domain stability and stabilization for stochastic Markovian switching systems driven by Wiener and Poisson noises

Shiyu Zhong, Weihai Zhang, Zhiguo Yan

2020International Journal of Robust and Nonlinear Control23 citationsDOI

Abstract

Abstract This paper studies finite‐time annular domain stability (FTADS) and stabilization for stochastic Markovian switching systems driven by both Wiener and Poisson noises. Firstly, new sufficient conditions, based on the common parameter approach (CPA)/mode‐dependent parameter approach (MDPA), are presented to make the stochastic Markovian switching systems FTADS. Secondly, the finite‐time annular domain stabilization (FTAD‐stabilization) is discussed. The state feedback controller (SFC) and the dynamic output feedback controller (DOFC) are designed by CPA/MDPA, respectively, and some new sufficient conditions are given for the existence of these controllers. Moreover, an algorithm is presented to find the value ranges of some parameters, which shows the superiority of MDPA. Finally, a numerical example is supplied to verify the validity of our results.

Topics & Concepts

Control theory (sociology)Stability (learning theory)Domain (mathematical analysis)Markov processController (irrigation)Poisson distributionTime domainMathematicsState (computer science)Computer scienceControl (management)AlgorithmMathematical analysisArtificial intelligenceBiologyComputer visionStatisticsAgronomyMachine learningStability and Control of Uncertain SystemsStability and Controllability of Differential EquationsControl and Stability of Dynamical Systems