• Journal of Institute of Control, Robotics and Systems
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• v.18 no.7
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• pp.613-616
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• 2012

This paper proposes the state observer design for nonlinear systems with delayed output. It is shown that by considering a nonlinear term of error dynamics as an additional state variable, the nonlinear error dynamics with time delay can be transformed into the linear one with time delay. Sufficient conditions for existence of a state observer are characterized by linear matrix inequalities. Finally, an illustrative example is given in order to show the effectiveness of our design method.

• Journal of Mechanical Science and Technology
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• v.20 no.6
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• pp.759-769
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• 2006

This paper proposes a new method of discretization for nonlinear systems using a Taylor series expansion and the zero-order hold assumption. The method is applied to sampled-data representations of nonlinear systems with input time delays. The delayed input varies in time and its amplitude is bounded. The maximum time-delayed input is assumed to be two sampling periods. The mathematical expressions of the discretization method are presented and the ability of the algorithm is tested using several examples. A computer simulation is used to demonstrate that the proposed algorithm accurately discretizes nonlinear systems with variable time-delayed inputs.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.4
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• pp.413-419
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• 2009

A decentralized adaptive control method is proposed for large-scale systems with unknown time-delayed nonlinear interconnections unmatched in control inputs. It is assumed that the time-delayed interaction terms are bounded by unknown nonlinear bounding functions. The nonlinear bounding functions and uncertain nonlinear functions of large-scale systems are compensated by the function approximation technique using neural networks. The dynamic surface control method is extended to design the proposed memoryless local controller for each subsystem of uncertain nonlinear large-scale time delay systems. Therefore, although the interconnected systems consist of a large number of subsystems, the proposed controller can be designed simply. We prove that all the signals in the total closed-loop system are semiglobally uniformly bounded and the control errors converge to an adjustable neighborhood of the origin. Finally, an example is given to demonstrate the effectiveness and applicability of the proposed scheme.

• International Journal of Control, Automation, and Systems
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• v.6 no.1
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• pp.24-34
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• 2008

A novel neural network model, termed the standard neural network model (SNNM), similar to the nominal model in linear robust control theory, is suggested to facilitate the synthesis of controllers for delayed (or non-delayed) nonlinear systems composed of neural networks. The model is composed of a linear dynamic system and a bounded static delayed (or non-delayed) nonlinear operator. Based on the global asymptotic stability analysis of SNNMs, Static state-feedback controller and dynamic output feedback controller are designed for the SNNMs to stabilize the closed-loop systems, respectively. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. Most neural-network-based nonlinear systems with time delays or without time delays can be transformed into the SNNMs for controller synthesis in a unified way. Two application examples are given where the SNNMs are employed to synthesize the feedback stabilizing controllers for an SISO nonlinear system modeled by the neural network, and for a chaotic neural network, respectively. Through these examples, it is demonstrated that the SNNM not only makes controller synthesis of neural-network-based systems much easier, but also provides a new approach to the synthesis of the controllers for the other type of nonlinear systems.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1107-1120
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• 2004

This study proposes a new scheme for the sampled-data representation of nonlinear systems with time-delayed multi-input. The proposed scheme is based on the Taylor-series expansion and zero-order hold assumption. The mathematical structure of a new discretization scheme is explored. On the basis of this structure, the sampled-data representation of nonlinear systems including time-delay is derived. The new scheme is applied to nonlinear systems with two inputs and then the delayed multi-input general equation is derived. The resulting time-discretization provides a finite-dimensional representation of nonlinear control systems with time-delay enabling existing controller design techniques to be applied to them. In order to evaluate the tracking performance of the proposed scheme, an algorithm is tested for some of the examples including maneuvering of an automobile and a 2-DOF mechanical system.

• Transactions on Control, Automation and Systems Engineering
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• v.2 no.4
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• pp.248-254
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• 2000

This paper presents and output feedback fuzzy H(sup)$\infty$ control problem for a class of nonlinear systems with time-varying delayed state. The Takagi-Sugeno fuzzy model is employed to represent a nonlinear systems with time-varying delayed state. Using a single quadratic Lyapunov function, the globally exponential stability and disturance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of fuzzy H(sup)$\infty$ controllers are given in terms of matrix inequalities. Constructive algorithm for design of fuzzy H(sup)$\infty$ controller is also developed. A simulation example is given to illustrate the performance of the proposed design method.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.972-975
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• 1996

This paper presents a sufficient condition for robust stability of discrete-time systems with delayed nonlinear perturbations. Using state evolution method, the bound on the norms of nonlinear perturbation which guarantees the exponential stability of the systems, is found. The numerical example is given to illustrate the results.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.1975-1987
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• 2005

An input time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computers. In this paper a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed. The mathematical structure of the new discretization method is analyzed. On the basis of this structure the sampled-data representation of nonlinear systems with time-delayed multi-input is presented. The delayed multi-input general equation has been derived. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. Additionally, hybrid discretization schemes that result from a combination of the scaling and squaring technique (SST) with the Taylor series expansion are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method's parameters to meet CPU time and accuracy requirements, are examined as well. A performance of the proposed method is evaluated using a nonlinear system with time delay maneuvering an automobile.

• Transactions on Control, Automation and Systems Engineering
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• v.1 no.2
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• pp.99-105
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• 1999

This paper presents a fuzzy H$\infty$ filtering problem for a class of uncertain nonlinear systems with time-varying delayed states and unknown inital state on the basis of Takagi-Sugeno(T-S) fuzzy model. The nonlinear systems are represented by T-S fuzzy models, and the fuzzy control systems utilize the concept of the so-called parallel distributed compensation. Using a single quadraic Lyapunov function, the stability and L2 gain performance from the noise signals to the estimation error are discussed. Sufficient conditions for the existence of fuzzy H$\infty$ filters are given in terms of linear matrix inequalities (LMIs). The filtering gains can also be directly obtained from the solutions of LMIs.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.7
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• pp.578-583
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• 2002

This paper presents a method for designing fuzzy $H_2/H_{\infty}$ controllers of nonlinear systems with time varying delay. Takagi-Sugeno fuzzy model is employed to represent nonlinear systems with time varying delay. Using a single quadratic Lyapunov function, the globally exponential stability and $H_2/H_{\infty}$ performance problem are discussed. A sufficient condition for the existence of fuzzy $H_2/H_{\infty}$ controllers is then presented in terms of linear matrix inequalities(LMls). The proposed fuzzy $H_2/H_{\infty}$ controllers minimizes the upper bound on the linear quadratic performance measure.