Bum Yong Park

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.

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.

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.

Control design of nonlinear systems over a communication network

This paper investigates a method for controlling a class of nonlinear systems over a communication network with the consideration of network-induced and sampling time delays, packet losses, and quantization errors. In order to represent continuous-time nonlinear systems, Takagi-Sugeno (T-S) fuzzy model is employed, based on which a networked control system (NCS) is designed so that all the states of the closed-loop system exponentially converge to a bounded ellipsoid. In this derivation, some useful techniques are systematically used to obtain a less conservative result. Finally, the effectiveness of the proposed approach is verif ed through an application example.

LPV controller design with multiple parameters for the nonlinear RTAC system

This paper proposes linear parameter varying (LPV) model with multiple parameters (LPV-MP) and statefeedback controller for the nonlinear rotational and translational actuator (RTAC) benchmark problem. First, based on LPV-MP, the conditions used for designing the state-feedback controller are formulated in terms of parameterized linear matrix inequalities (PLMIs) and the state-feedback LPV controller using multiple parameters-dependent Lyapunov function (MPDLF) is designed. Then, PLMI conditions are converted into linear matrix inequalities (LMIs) by using a parameter relaxation technique. The proposed method results in the reduced decision variables and simulation results show good performance of the proposed method.