In Seok Park

Improved H∞ state-feedback control for continuous-time Markovian jump fuzzy systems with incomplete knowledge of transition probabilities☆

Abstract This paper proposes the improved H ∞ state-feedback control for Markovian jump fuzzy systems (MJFSs) with incomplete knowledge of transition probabilities. From the fundamental first-order properties of the transition rates, two second-order properties are introduced without information on the lower and upper bounds of the transition rates, differently from other approaches in the literature. Based on these properties, this paper uses all possible slack variables into the relaxation process which contributes to reduce the conservatism. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

H control for singular Markovian jump systems with incomplete knowledge of transition probabilities

This paper proposes a H state-feedback control for singular Markovian jump systems with incomplete knowledge of transition probabilities. Different from the previous results where the transition rates are completely known or the bounds of the unknown transition rates are given, a more general situation where the transition rates are partly unknown and the bounds of the unknown transition rates are also unknown is considered. Moreover, in contrast to the singular Markovian jump systems studied recently, the proposed method does not require any tuning parameters that arise when handling non-convex terms related to the mode-dependent Lyapunov matrices and the corresponding self-mode transition rates. Also, this paper uses all possible slack variables related to the transition rates into the relaxation process which contributes to reduce the conservatism. Finally, two numerical examples are provided to demonstrate the performance of H mode-dependent control.

Dynamic Output-Feedback Control for Singular Markovian Jump System: LMI Approach

For the dynamic output-feedback stabilization of continuous-time singular Markovian jump systems, this paper introduces the necessary and sufficient condition, whereas the previous research works suggested the sufficient conditions. A special choice of the block entries of Lyapunov matrices leads to derive the necessary and sufficient condition in terms of linear matrix inequalities. A numerical example shows the validity of the derived results.

H∞ control for Markovian jump fuzzy systems with partly unknown transition rates and input saturation

Abstract This paper considers less conservative conditions of H ∞ control for Markovian jump fuzzy systems (MJFSs) with partly unknown transition rates and input saturation. To find H ∞ control for level γ, a set invariance condition and the stabilization conditions are first formulated in terms of parameterized linear matrix inequalities (PLMIs) by considering the properties of transition rates. Then, to derive the less conservative stabilization conditions, all possible slack variables are incorporated into the relaxation process with fully considering the property of the fuzzy weights. Two numerical examples are provided to illustrate the effectiveness of the proposed method.

Stabilization of positive Markovian jump systems with input saturation: A linear programming approach

This paper proposes a linear programming (LP) approach for stabilization of positive Markovian jump systems (PMJSs) with input saturation. First of all, we derive the sufficient conditions for stabilization of PMJSs with input saturation based on the linear co-positive Lyapunov function. However, since the decision variables in the obtained conditions are mutually coupled, the conditions are not linear. Therefore, to obtain the condition that can be solved by the LP, we propose the methods to properly choose the decision variables. Furthermore, we give a process to acquire the largest domain of attraction. Finally, we suggest two numerical examples to illustrate the validity of the proposed methods.

Output-feedback control for singular Markovian jump systems

In this paper, the stabilization problem for continuous-time singular Markovian jump systems with unmeasurable states is investigated. Differently from the previous researches, the dynamic output-feedback stabilization conditions are formulated in terms of strict linear matrix inequalities by using variable elimination lemma and new partitioning method about mode-dependent Lyapunov matrices. Numerical examples are provided to demonstrate the validity of the derived results.

H 2 control for discrete-time Markovian jump fuzzy systems with partly known transition probabilities (ICCAS 2016)

In this paper, the H2 control for discrete-time Markovian jump fuzzy system (MJFS) with partly known transition probabilities is considered. To deal with unknown transition probabilities, convex property of the normalized unknown transition probabilities and lower bound lemma for the inversion of the matrix summation are used. Then, using the properties of fuzzy weights, quadratic condition of stochastic stability and guaranteed cost is obtained. Finally, linear matrix inequalities (LMIs) are derived from the quadratic condition. In order to illustrate the effectiveness of the proposed theorem, the practical problem is given as a numerical example.

ℋ ∞ state-feedback control for continuous-time Markovian jump systems with partly unknown transition probabilities(ICCAS 2015)

This paper considers the ℋ∞ state-feedback control for continuous-time Markovian jump systems with partly unknown transition probabilities. The aim of this paper is to derive the ℋ∞ stabilization condition such that the MJS with partly unknown transition probabilities is stochastically stable with γ-disturbance attenuation. First of all, the transition rates associated with the transition probabilities are expressed in terms of the three properties without the lower and upper bounds of the transition rates, differently from other approaches in the literature. Then, with consideration of the properties of transition rates, the ℋ∞ stabilization conditions are derived in the quadratic form. And then the quadratic form can be replaced by the linear matrix inequalities(LMIs). Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.