• Journal of IKEEE
• /
• v.18 no.2
• /
• pp.255-262
• /
• 2014

The uncertain integral linear system is the integral-augmented uncertain system to improve the resultant performance. In this note, for a MI(Multi Input) uncertain integral linear case, Utkin's theorem is proved clearly and comparatively. With respect to the two transformations(diagonalizations), the equation of the sliding mode is invariant. By using the results of this note, in the SMC for MIMO uncertain integral linear systems, the existence condition of the sliding mode on the predetermined sliding surface is easily proved. The effectiveness of the main results is verified through an illustrative example and simulation study.

• 제어로봇시스템학회:학술대회논문집
• /
• 1991.10a
• /
• pp.55-59
• /
• 1991

This paper presents a method for designing a full state feedback linear static control law. This will stabilize a given linear uncertain system and also guarantee the performance of the system. The uncertain systems are described by state equation which contains uncertain parameters in system and input distribution matrices. The method is based on the guaranteed cost control of Chang and Peng(1972). The controller gain can be obtained by the solution of a algebraic Riccati equation in which the input weighting matrices depend on the uncertainty bounds. The algebraic Riecati equation in this paper is same as that of weighted LQ regulator problem.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.48 no.2
• /
• pp.153-158
• /
• 1999

We consider single-input nonlinear systems with unknown unmodelled time-varying parameters or disturbances which are bounded. The main goal is to identify classes of uncertain systems for which the control exist and to provide constructive design procedures. Assuming that the undisturbed nominal system ( ,g) is partially state feedback linearizable, that a strict triangularity condition, a linear parametrization condition, and {{{{ { G}_{r-1 } }}}} hold for the uncertain terms, and that some condition is satisfied in the transformed partially linear system, we design an adaptive regulating dynamic control. At first, we identify classes of nonlinear uncertain systems and give a systematic procedure for the design of a robust regulation for the nonlinear systems.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2000.11a
• /
• pp.476-479
• /
• 2000

This paper deals with a robust pole placement method for uncertain linear systems. For all admissible uncertain parameters, a static output feedback controller is designed such that all the poles of the closed loop system are located within the prespecfied disk. It is shown that the existence of a positive definite matrix belonging to a convex set such that its inverse belongs to another convex set guarantees the existence of the output feedback gain matrix for our control problem. By a sequence of convex optimization the aforementioned matrix is obtained. A numerical example is solved in order to illustrate efficacy of our design method.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.48 no.5
• /
• pp.553-559
• /
• 1999

The robust control problem of the linear systems with uncertainty is classified as the robust stability problem guaranteeing the stability and the robust performance problem guaranteeing the disired performance. In this paper, we considered the robust performance analysis problem, which find the upper buund of the quadratic performance of the uncertain linear system, and the robust guaranteed performance controller design problem which design a controller guaranteeing the desired quadratic performance. At first, we treated the analysis problem and presented the two results; one is dependent on the performance of the nominal system and another is independent on this. And we treated the design method guaranteeing the desired performance for the uncertain linear systems, Finally, we show the usefulness of our results by numerical examples.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.59 no.6
• /
• pp.1173-1178
• /
• 2010

In this note, a systematic design of a new robust nonlinear integral variable structure controller based on state dependent nonlinear form is presented for the control of uncertain more affine nonlinear systems with mismatched uncertainties and matched disturbance. After an affine uncertain nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a new robust nonlinear integral variable structure controller is presented. To be linear in the closed loop resultant dynamics and remove the reaching phase problems, the linear integral sliding surface is suggested. A corresponding control input is proposed to satisfy the closed loop exponential stability and the existence condition of the sliding mode on the linear integral sliding surface, which will be investigated in Theorem 1. Through a design example and simulation studies, the usefulness of the proposed controller is verified.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.60 no.9
• /
• pp.1754-1760
• /
• 2011

In this paper, a systematic design of a robust nonlinear multivariable variable structure controller based on state dependent nonlinear form is presented for the control of MIMO uncertain affine nonlinear systems with mismatched uncertainties and matched disturbance. After a MIMO uncertain affine nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the linear sliding surface is applied. A corresponding diagonalized control input is proposed to satisfy the closed loop global exponential stability and the existence condition of the sliding mode on the linear sliding surface, which will be investigated in Theorem 1. Through a design example and simulation study, the usefulness of the proposed controller is verified.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.59 no.5
• /
• pp.945-949
• /
• 2010

In this paper, a systematic design of a new robust nonlinear variable structure controller based on state dependent nonlinear form is presented for the control of uncertain affine nonlinear systems with mismatched uncertainties and matched disturbance. After an affine uncertain nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a new robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the linear sliding surface is applied. A corresponding control input is proposed to satisfy the closed loop exponential stability and the existence condition of the sliding mode on the linear sliding surface, which will be investigated in Theorem 1. Through a design example and simulation study, the usefulness of the proposed controller is verified.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2005.11a
• /
• pp.95-98
• /
• 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 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 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 the digitally controlled system are formulated in terms of linear matrix inequalities (LMls). Finally, we prove the effectiveness and stabilization of the proposed intelligent digital redesign method by applying the chaotic Lorentz system.

• Proceedings of the KIEE Conference
• /
• 2005.10b
• /
• pp.496-498
• /
• 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 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 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 the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs).