Quantised control of delayed Markovian jump systems with partly known transition probabilities

Abstract

Abstract This paper is devoted to solve the quantised control problem of the continuous‐time uncertain Markovian jump systems with mixed time delays and partly known transition probabilities. For the Markov chain, the transition rates are assumed to be partly known. The involved mixed time delays comprise both time‐varying delays and distributed delays. The logarithmic quantiser is introduced in the design of the state feedback controller and the uncertainty is entered into the quantization error matrix represented by an interval matrix. Based on the generalised Itô's formula, the free‐connection weighting matrix method and the stochastic analysis theory, several novel sufficient conditions are derived to guarantee that the trivial solution of the closed‐loop system is robustly exponentially stable in the mean square. Then, the concrete expression form of the desired controller gain is obtained via the solutions to a set of linear matrix inequalities. In addition, the corresponding stability criteria are given for three special situations of Markovian jump systems. Finally, a numerical example and a practical example (the wheeled mobile manipulator) are provided to show the feasibility and availability of the proposed theoretical results.

Keywords

• Algebra
• Markov processes
• Other topics in statistics
• Linear control systems
• Control system analysis and synthesis methods
• Stability in control theory