Nam Kyu Kwon

Stabilization of Markovian jump systems with incomplete knowledge of transition probabilities and input quantization

Abstract This paper introduces the stabilization condition for the Markovian jump systems (MJSs) with incomplete knowledge of transition probabilities and input quantization. To obtain the less conservative stabilization condition, an appropriate weighting method is proposed by using all possible slack variables from the relationship of the transition probabilities, which does lead to a form of linear matrix inequalities (LMIs). Further, a proposed controller not only stabilizes the MJS with incomplete knowledge of transition probabilities but also eliminates the effect of input quantization. Simulation examples report the effectiveness of the proposed criterion.

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.

State-feedback control for LPV systems with interval uncertain parameters

Abstract This paper proposes a state-feedback controller design for linear parameter-varying systems with interval uncertain parameters that are interval-type uncertain weight functions for convex combinations of linear subsystems. The proposed controller hires secondary convex parameters generated through the lower and upper boundaries of the interval uncertain parameters. The resulting stabilization condition is expressed in terms of parameterized linear matrix inequalities, which are then converted into linear matrix inequalities using a parameter relaxation technique. The simulation results illustrate the robustness of the proposed controller.

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.

Improved ℋ ∞ state-feedback control for discrete-time Markovian jump systems with incomplete knowledge of transition probabilities(ICCAS 2015)

This paper considers improved ℋ∞ state-feedback control for discrete-time Markovian jump systems with incomplete knowledge of transition probabilities. To achieve the better ℋ∞ performance, this paper proposes two valuable approaches. First, under the assumption that the lower and upper bounds of unknown transition probabilities are known, the closed-loop stabilization conditions are represented as convex combination with these bounds. Second, a new lower bound lemma for the inversion of the matrix summation is investigated. This lemma enables the inversion of the matrix summation to be replaced by free variable which does not contain the transition probabilities. Thus, the ℋ∞ stabilization conditions consist of two parts which are transition probability independent part and dependent part. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

A bias-compensated affine projection algorithm for noisy input data

This paper proposes a bias-compensated affine projection algorithm (BC-APA) to eliminate bias due to noisy input data and to reduce the performance degradation due to highly correlated input data. A new affine projection algorithm (new APA) using innovative input data is presented for highly correlated input data. We analyze the bias in this innovative new APA under noisy input data and remove it. To remove the bias, an estimation method for the input noise variance is presented and explained. In simulations, the BC-APA provided both fast convergence rate and small mean square deviation. Based on improved precision to estimate a finite impulse response of an unknown system, the BC-APA can be applied extensively in adaptive signal processing areas.

Optimal H∞ filtering for singular Markovian jump systems

Abstract This paper considers H ∞ filtering for continuous-time singular Markovian jump systems (SMJSs). While the existing researches in the literature suggested only sufficient conditions in terms of strict or non-strict linear matrix inequalities (LMIs) for sub-optimal H ∞ filtering, this paper successfully derives a necessary and sufficient condition in terms of strict LMIs for optimal H ∞ filtering. First, the necessary and sufficient condition that guarantees the stochastic admissibility of the filtering error system is obtained in terms of matrix inequalities. To reformulate it into strict LMIs, the congruence transformation by specially designed matrices is used. Two numerical examples show the validity of proposed H ∞ filtering.

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.