Observer-based control for a singular Markovian jumping system

Abstract

Purpose For most practical control system problems, the state variables of a system are not often available or measureable due to technical or economical constraints. In these cases, an observer-based controller design problem, which is involved with using the available information on inputs and outputs to reconstruct the unmeasured states, is desirable, and it has been wide investigated in many practical applications. However, the investigation on a discrete-time singular Markovian jumping system is few so far. This paper aims to consider an observer-based control problem for a discrete-time singular Markovian jumping system and provides a set of easy-used conditions to the proposed control law. Design/methodology/approach According to the connotation of the separation principle extended from linear systems, a mode-dependent observer and a state-feedback controller is designed and carried out independently via two sets of derived necessary and sufficient conditions in terms of linear matrix inequalities (LMIs). Findings A set of necessary and sufficient conditions for an admissibility analysis problem related to a discrete-time singular Markovian jumping system is derived to be a doctrinal foundation for the proposed design problems. A mode-dependent observer and a controller for such systems could be designed via two sets of strictly LMI-based synthesis conditions. Research limitations/implications The proposed method can be applied to discrete-time singular Markovian jumping systems with transition probability pij > 0 rather than the ones with pii = 0. Practical implications The formulated problem and proposed methods have extensive applications in various fields such as power systems, electrical circuits, robot systems, chemical systems, networked control systems and interconnected large-scale systems. Take robotic networked control systems for example. It is recognized that the variance phenomena derived from network transmission, such as packets dropout, loss and disorder, are suitable for modeling as a system with Markovian jumping modes, while the dynamics of the robot systems can be described by singular systems. In addition, the packets dropout or loss might result in unreliable transmission signals which motivates an observer-based control problem. Originality/value Both of the resultant conditions of analysis and synthesis problems for a discrete-time singular Markovian jumping system are necessary and sufficient, and are formed in strict LMIs, which can be used and implemented easily via MATLAB toolbox.

An Observer-Based Controller Design for a Markovian Jumping Singular System with Polytopic Uncertainties

“…Remark 2. Comparing with our recent results (27) , there are two advantages and differences in this paper. One is that the assumption that C must be full-row-rank is unnecessary and is removed in this paper, which fits more practical cases.…”

“…This observation motivates our studies. In this paper, we extend our recent results (27) consider a mode dependent observer and controller co-design problem for a DMJSS with polytopic uncertainties. The contributions of this paper are as follows.…”

“…Lemma 1 which is an extension of Lemma 3 (27) is essential for our resultant conditions related to the corresponding analysis problems. Lemma 2 which is an extension of Lemma 4 (27) enables us to consider the observer design and the controller design problems independently. Lemma 3 provides us a key idea so that we can unify our methods for the design tasks.…”

“…The contributions of this paper are as follows. (a) We generalize problem formulation to a system with polytopic uncertainties and extend the resultant LMI-based conditions (27) for an admissibility analysis problem. (b) We unify a method to deal with two design tasks, and derive two sets of strictly LMI-based synthesis conditions for an observer and a controller.…”