Generalised absolute stability analysis and synthesis for Lur'e-type descriptor systems

Yang, Chunyu; Zhang, Q.; Zhou, Lei

doi:10.1049/iet-cta:20060349

Cited by 28 publications

(20 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Assume that Assumptions A1) and A3) hold, and that A2) holds for systems (23) and (24). If there exists a symmetric matrix K ∈ R m×m such that (5) holds, and g i = d i , i = 1, 2, then the following L 2 disturbance attenuation controller…”

Section: Theorem 31mentioning

confidence: 99%

“…Substituting u = −K(y − η) + v into systems (23) and (24), it can be seen from the proof of Theorem 2.7 that systems (23) and (24) are impulse controllable and can be expressed in the following dissipative Hamiltonian form:…”

Section: Theorem 31mentioning

confidence: 99%

“…From the proof of Theorem 3.1, we know that under u = −K(y − η) + v, systems (23) and (24) are impulse controllable and can be expressed as (26). According to Condition (2), we have…”

Section: Proofmentioning

confidence: 99%

“…It is easy to see that (30) is a sufficient but not a necessary condition under which controller (25) can simultaneously stabilize systems (23) and (24).…”

Section: Remark 33mentioning

confidence: 99%

“…Using the linear matrix inequality method, the generalized absolute stability was studied in ref. [24] for linear descriptor systems with feedback-connected nonlinearities. It should be pointed out that there are, to the authors' best knowledge, few works on the simultaneous stabilization of NDSs.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Simultaneous stabilization of a class of nonlinear descriptor systems via Hamiltonian function method

Sun

Wang

2009

Sci. China Ser. F-Inf. Sci.

View full text Add to dashboard Cite

This paper studies simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonian function method. Firstly, based on the Hamiltonian realization of the nonlinear descriptor systems and a suitable output feedback, two nonlinear descriptor systems are equivalently transformed into two nonlinear Hamiltonian differential-algebraic systems by a nonsingular transformation, and a sufficient condition for two closed-loop systems to be impulse-free is given. The two systems are then combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique, based on which a simultaneous stabilization controller and a robust simultaneous stabilization controller are designed for the two systems. Secondly, the case of more than two nonlinear descriptor systems is investigated, and two new results are proposed for the simultaneous stabilization and robust simultaneous stabilization, respectively. Finally, an illustrative example is studied by using the results proposed in this paper, and simulations show that the simultaneous stabilization controllers obtained in this paper work very well.nonlinear descriptor systems, simultaneous stabilization, robust simultaneous stabilization, Hamiltonian function method

show abstract

Section: Theorem 31mentioning

confidence: 99%

Section: Theorem 31mentioning

confidence: 99%

“…From the proof of Theorem 3.1, we know that under u = −K(y − η) + v, systems (23) and (24) are impulse controllable and can be expressed as (26). According to Condition (2), we have…”

Section: Proofmentioning

confidence: 99%

“…It is easy to see that (30) is a sufficient but not a necessary condition under which controller (25) can simultaneously stabilize systems (23) and (24).…”

Section: Remark 33mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Simultaneous stabilization of a class of nonlinear descriptor systems via Hamiltonian function method

Sun

Wang

2009

Sci. China Ser. F-Inf. Sci.

View full text Add to dashboard Cite

show abstract

Strongly absolute stability of Lur'e descriptor systems: Popov‐type criteria

Yang

Zhang

Zhou

2008

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

SUMMARYIn this paper, we consider the strongly absolute stability problem of Lur'e descriptor systems (LDSs). First, we define a generalized Lur'e Lyapunov function (GLLF) and show that the negative-definite property of the derivative of the GLLF guarantees strongly absolute stability of LDSs. As a result, the existing Popov-type criteria are reduced to sufficient conditions for the existence of the GLLF. Then, we propose a necessary and sufficient condition for the existence of the GLLF to guarantee the strongly absolute stability of LDSs. This criterion is shown to be less conservative than the existing ones. Finally, we discuss the computational issues and present two numerical examples to illustrate the effectiveness of the obtained results.

show abstract

Improved delay-dependent absolute stability and robust stability for a class of nonlinear systems with a time-varying delay

Zhang

et al. 2009

Int. J. Robust Nonlinear Control

View full text Add to dashboard Cite

SUMMARYThis paper investigates the problem of the absolute stability of Lur'e systems with a time-varying delay. By considering the relationships among the time-varying delay, its upper bound, and the difference between them, less conservative delaydependent stability criteria are obtained and formulated in terms of linear matrix inequalities, without ignoring any useful terms in the derivative of a Lyapunov-Krasovskii functional. Numerical example shows that the results obtained in this paper are better than the previous results.

show abstract

Generalised absolute stability analysis and synthesis for Lur'e-type descriptor systems

Cited by 28 publications

References 18 publications

Simultaneous stabilization of a class of nonlinear descriptor systems via Hamiltonian function method

Simultaneous stabilization of a class of nonlinear descriptor systems via Hamiltonian function method

Strongly absolute stability of Lur'e descriptor systems: Popov‐type criteria

Improved delay-dependent absolute stability and robust stability for a class of nonlinear systems with a time-varying delay

Contact Info

Product

Resources

About