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Amirhossein Abolmasoumi

Amirhossein Abolmasoumi

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0001-9739-1340
Education: PhD.
ScopusId: 26664422200
Faculty: Engineering
Address: Arak University
Phone:

Research

Title
An adaptive sliding mode approach for Markovian jump systems with uncertain mode-dependent time-varying delays and partly unknown transition probabilities
Type
JournalPaper
Keywords
Linear matrix inequality (LMI) · Markovian jump systems (MJSs) · Mode-dependent time-varying delay · Partly unknown transition probabilities · Sliding mode control · Stochastic stability
Year
2019
Journal International Journal of Dynamics and Control
DOI
Researchers Amirhossein Abolmasoumi ، Nasibeh Zohrabi ، Hamid Reza Momeni ، Hassan Zakeri

Abstract

This paper deals with the problems of stochastic stability and sliding mode control for a class of continuous-time Markovian jump systems with mode-dependent time-varying delays and partly unknown transition probabilities. The design method is general enough to cover a wide spectrum of systems from those with completely known transition probability rates to those with completely unknown transition probability rates. Based on some mode-dependent Lyapunov–Krasovski functionals and making use of the free-connection weighting matrices, new delay-dependent conditions guaranteeing the existence of linear switching surfaces and the stochastic stability of sliding mode dynamics are derived in terms of linear matrix inequalities (LMIs). Then, a sliding mode controller is designed such that the resulted closed-loop system’s trajectories converge to predefined sliding surfaces in a finite time and remain there for all subsequent times. This paper also proposes an adaptive sliding mode controller design method which applies to cases in which mode-dependent time-varying delays are unknown. All the conditions obtained in this paper are in terms of LMI feasibility problems. Numerical examples are given to illustrate the effectiveness of the proposed methods.