• Transactions on Control, Automation and Systems Engineering
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• v.4 no.2
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• pp.140-146
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• 2002

We consider a class of large-scale interconnected time delay systems and investigate a decentralized robust passive control problem. sufficient conditions for unforced interconnected uncertain systems with time delay to be robustly stable with extended strictly passivity is given in terms of algebraic Riccati inequality and linear matrix inequality. The decentralized robust passive control problem for norm-bounded and positive real uncertainty is shown to be converted to extended strictly positive real control problem for a modified system which contains neither time delay nor uncertainty.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.1
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• pp.1-10
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• 1999

We consider the problem of synthesizing an internally stabilizing linear time-invariant controller for a linear tune-Invariant plant such that a given closed loop transfer function is strictly sector bounded. We show that the standard $H{\infty}$ control problem and the $\tau$ -positive real control problem are special cases of sector bounded control problem. Necessary and sufficient conditions for the existence of a controller are obtained. The state-space representation for strictly proper controllers are given in terms of solutions to ARIs or AREs.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.2
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• pp.157-162
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• 1998

This paper provides some properties of positive real systems in time domain. It is well-known that a positive real system and a bounded real system are closely related by bilinear transform in a frequency domain. By using supply rate and storage function, we show that a positive real system can be transformed into a bounded real system, and that a positive real system can be transformed into another positive real system with in a time domain. Also, we show that an ESPR(extended strictly positive real) system can be decomposed into a feedback system of lossless positive real system and another ESPR system. These results may be used to design an output feedback controller for mixed H$H_2$ESPR problem.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.9
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• pp.50-59
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• 1997

This paper is on the generalized singular perturbation approximation (GSPA) preserving the discrete positive real property. We transform the discrete positive real(PR) system into a stochastically banlanced system and get the reduced order discrete system from the GSPA of the full order stochastically balanced system. eSPECIALLY, WHEN THE FREE PARAMETER OF THE gspa IS .+-.1, we show that the reduced order discrete system retains stability, minimality, and positive real and stochstically balancing properties. And we derived the .inf.-norm error bound with the reduced order discrete strictly positive real(SPR) system by the proposed method. Finally, we give an example to ascertain the properties of the proposed reduced order discrete system and to compare with the conventional methods.

• International Journal of Control, Automation, and Systems
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• v.3 no.2
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• pp.195-201
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• 2005

This paper discusses the problem of positive real control for uncertain 2-D linear discrete time singular Roesser models (2-D SRM) with time-invariant norm-bounded parameter uncertainty. The purpose of this study is to design a state feedback controller such that the resulting closed-loop system is acceptable, jump modes free and stable, and achieves the extended strictly positive realness for all admissible uncertainties. A version of positive real lemma for the 2-D SRM is given in terms of linear matrix inequalities (LMIs). Based on the lemma, a sufficient condition for the solvability of the positive real control problem is derived in terms of bilinear matrix inequalities (BMIs) and an iterative procedure for solving the BMIs is proposed.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.9
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• pp.520-525
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• 2003

A robust controller for large space structures(LSS) is studied from passivity point of view. While velocity sensors are commonly used for proportional-derivative (PD) control law to stabilize large space structures, if the structure can be controlled without velocity measurements, it is desirable against the failure of velocity sensors and for the cost reduction of the sensing system. In a recent result a dynamic output feedback control law has been provided using only displacement measurements. This paper presents a passivity-based controller design method and provides an alternative stability analysis tool for the previous displacement feedback robust control law. The closed-loop system can be viewed as a feedback interconnection of a passivated large space structure (LSS) and a strictly positive real (SPR) system.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1150-1158
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• 2004

In this paper, we present an adaptive observer for nonlinear systems that include unknown constant parameters and are not necessarily observable. Sufficient conditions are given for a nonlinear system to be transformed by state-space change of coordinates into an adaptive observer canonical form. Once a nonlinear system is transformed into the proposed adaptive observer canonical form, an adaptive observer can be designed under the assumption that a certain system is strictly positive real. An illustrative example is included to show the effectiveness of the proposed method.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.309-317
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• 2016

Let V be a Euclidean Jordan algebra with a symmetric cone K. We show that for a Z-transformation L with the additional property L(K) ⊆ K (which we will call ’cone-preserving’), GUS ⇔ strictly copositive on K ⇔ monotone + P. Specializing the result to the Stein transformation S_A(X) := X - AXA^T on the space of real symmetric matrices with the property $S_A(S^n_+){\subseteq}S^n_+$, we deduce that S_A GUS ⇔ I ± A positive definite.

• Kyungpook Mathematical Journal
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• v.51 no.3
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• pp.345-352
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• 2011

In this article we introduce the fuzzy real valued double sequence spaces $_2{\ell}^F$ (p) where p = ($p_{nk}$) is a double sequence of bounded strictly positive numbers. We study their different properties like completeness, solidness, symmetricity, convergence free etc. We prove some inclusion results also.

• Journal of IKEEE
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• v.7 no.2 s.13
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• pp.156-165
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• 2003

This paper describes the design of a robust adaptive fuzzy observer for uncertain nonlinear dynamical system. We propose a new method in which no strictly positive real (SPR) condition is needed. No a priori knowledge of an upper bound on the lumped uncertainty is required. The Lyapunov synthesis approach is used to guarantee a semi-global uniform ultimate boundedness property of the state observation error, as well as of all other signals in the closed-loop system. The theoretical results are illustrated through a simulation example of a mass-spring-damper system.