• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2001.12a
• /
• pp.153-156
• /
• 2001

This paper discusses a stochastic stabilization of Takagi-Sugeno (75) fuzzy system with Markovian input delay. The finite Markovian process is adopted to model the input delay of the overall control system. It is assumed that the zero and hold devices are used for control input. The continuous-time 75 fuzzy system with the Markovian input delay is discretized for easy handling delay, accordingly, the discretized 75 fuzzy system is represented by a discrete-time 75 fuzzy system with jumping parameters. The stochastic stabilizibility of the jump 75 fuzzy system is derived and formulated in terms of linear matrix inequalities (LMls).

• Journal of Advanced Navigation Technology
• /
• v.23 no.6
• /
• pp.577-583
• /
• 2019

A dynamic system is called positive if any trajectory of the system starting from non-negative initial states remains forever non-negative for non-negative controls. In this paper, we consider the new stability condition for the positive time-varying linear discrete interval systems with time-varying delay and unstructured uncertainty. The delay time is considered as time-varying within certain interval having minimum and maximum values and the system is subjected to nonlinear unstructured uncertainty which only gives information on uncertainty magnitude. The proposed stability condition is an improvement of the previous results which can be applied only to time-invariant systems or had no consideration of uncertainty, and they can be expressed in the form of a very simple inequality. The stability conditions are derived using the Lyapunov stability theory and have many advantages over previous results using the upper solution bound of the Lyapunov equation. Through numerical example, the proposed stability conditions are proven to be effective and can include the existing results.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.15 no.7
• /
• pp.881-886
• /
• 2005

This paper presents intelligent digital redesign method of global approach for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent tile complex system. And global approach design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between nonlinearly interpolated linear operators to be matched. Also, by using the power series, we analyzed nonlinear system's uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the global state-matching of tile digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). Finally, a TS fuzzy model for the chaotic Lorentz system is used as an example to guarantee the stability and effectiveness of the proposed method.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.16 no.2
• /
• pp.138-143
• /
• 2006

This paper presents intelligent digital redesign method for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent the complex system. And global approach design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between nonlinearly interpolated linear operators to be matched. Also, by using the bilinear and inverse bilinear approximation method, we analyzed nonlinear system's uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the global state-matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). Finally, a TS fuzzy model for the chaotic Lorentz system is used as an . example to guarantee the stability and effectiveness of the proposed method.

• Proceedings of the KIEE Conference
• /
• 2000.07d
• /
• pp.2602-2604
• /
• 2000

In this paper, we study robust linear optimal model following servo system in the presence of disturbances and parameter perturbations. A technique to directly design the generalized differential operator based unified control system that covers both differential operator based continuous time and delta operator based discrete time case is presented. The quadratic criterion function for a linear system is used to design the robust unified servo control system. This servo control system is designed by applying a simple genetic algorithm to follow the output of the reference model optimally. The characteristics of the proposed servo system are analysed and simulated to verify the robustness.

• Journal of Institute of Control, Robotics and Systems
• /
• v.5 no.2
• /
• pp.131-138
• /
• 1999

In discrete-time controlled system, sampling time is one of the critical parameters for control performance. It is useful to employ different sampling rates into the system considering the feasibility of measuring system or actuating system. The systems with the different sampling rates in their input and output channels are named multirate system. Even though the original continuous-time system is time-invariant, it is realized as time-varying state equation depending on multirate sampling mechanism. By means of the augmentation of the inputs and the outputs over one Period, the time-varying system equation can be constructed into the time-invariant equation. In this paper, an alternative time-invariant model is proposed, the design method and the stability of the LQG (Linear Quadratic Gaussian) control scheme for the realization are presented. The realization is flexible to construct to the sampling rate variations, the closed-loop system is shown to be asymptotically stable even in the inter-sampling intervals and it has smaller computation in on-line control loop than the previous time-invariant realizations.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.46 no.3
• /
• pp.15-21
• /
• 2009

In this paper, we consider the design problem of robust stabilization and robust guaranteed cost state feedback controller for discrete-time singular systems with parameter uncertainties by LMI(linear matrix inequality) approach without semi-definite condition and decomposition of system matrices. The objective of robust stabilization controller is to construct a state feedback controller such that the closed-loop system is regular, causal, and stable. In the case of robust guaranteed cost control, the optimal value of guaranteed cost and controller design method are presented on the basis of robust stabilization control technique. Finally, a numerical example is provided to show the validity of the design methods.

• Journal of Institute of Control, Robotics and Systems
• /
• v.17 no.2
• /
• pp.139-144
• /
• 2011

We consider the stabilization problem for a class of networked control systems with random delays in the discrete-time domain. The controller-to-actuator and sensor-to-controller time-delays are modeled as two Markov chains, and the resulting closed-loop systems are Markovian jump nonlinear systems with two modes. The T-S (Takagi-Sugeno) fuzzy model is employed to represent a nonlinear system with Markovian jump parameters. The aim is to design a fuzzy controller such that the closed-loop Markovian jump fuzzy system is stochastically stable. The necessary and sufficient conditions on the existence of stabilizing fuzzy controllers are established in terms of LMIs (Linear Matrix Inequalities). It is shown that fuzzy controller gains are mode-dependent. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method.

• Journal of Power Electronics
• /
• v.19 no.4
• /
• pp.1000-1010
• /
• 2019

The use of internal-model-based linear controller, such as resonant controller, is a well-established technique for the current control of grid-connected systems. Attractive properties for resonant controllers include their two-sequence tracking ability, the simple control structure, and the reduced computational burden. However, in the case of continuous-designed resonant controller, the transient performance is inevitably degraded at a low switching frequency. Moreover, available design methods for resonant controller is not able to realize the direct design of transient performances, and the anticipated transient performance is mainly achieved through trial and error. To address these problems, the zero-order-hold (ZOH) characteristic and inherent time delay in digital control systems are considered comprehensively in the design, and a corresponding hold-equivalent discrete model of the grid-connected converter is then established. The relationship between the placement of closed-loop poles and the corresponding transient performance is comprehensively investigated to realize the direct mapping relationship between the control gain and the transient response time. For the benefit of automatic tuning and real-time adaption, analytical expressions for controller gains are derived in detail using the required transient response time and system parameters. Simulation and experimental results demonstrate the validity of the proposed method.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.39 no.5
• /
• pp.26-33
• /
• 2002

The design method of robust $H_{\infty}$ filtering for discrete-time uncertain linear systems is investigated in this paper. The uncertain parameters are assumed to be unknown but belonging to known convex compact set of polytope type. The objective is to design a stable robust $H_{\infty}$ filter guaranteeing the asymptotic stability of filtering error dynamics and present an $L_2$ induced norm bound analytically for the modified $H_{\infty}$ performance measure. The sufficient condition for the existence of robust $H_{\infty}$ filter and the filter design method are established by LMI(linear matrix inequality) approach, which can be solved efficiently by convex optimization. The proposed algorithm is checked through an example.