Vahid Samadi Bokharaie

D-Stability and Delay-Independent Stability of Homogeneous Cooperative Systems

We introduce a nonlinear definition of D-stability, extending the usual concept for positive linear time-invariant systems. We show that globally asymptotically stable, cooperative systems, homogeneous of any order with respect to arbitrary dilation maps are D-stable. We also prove a strong stability result for delayed cooperative homogeneous systems. Finally, we show that both of these results also hold for planar cooperative systems without the restriction of homogeneity.

Stability and D-stability for Switched Positive Systems

We consider a number of questions pertaining to the stability of positive switched linear systems. Recent results on common quadratic, diagonal, and copositive Lyapunov function existence are reviewed and their connection to the stability properties of switched positive linear systems is highlighted. We also generalise the concept of D-stability to positive switched linear systems and present some preliminary results on this topic.

On Delay-Independent Stability of a Class of Nonlinear Positive Time-Delay Systems

We present a condition for delay-independent stability of a class of nonlinear positive systems. This result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems.

Small-signal stability analysis of delayed power system stabilizers

This paper presents a stability analysis of power system stabilizers (PSS) for synchronous generators with inclusion of time delays. The paper shows that a time delay in the PSS feedback loop can improve the small-signal stability of a power system if the regulator gain is properly tuned. The paper provides a proof-of-principle analysis based on the classical model of the synchronous machine as well as a case study based on a detailed transient model of the IEEE 14-bus test system. The paper also provides a discussion on the practical implications that the properties of delayed PSS can have on the control of synchronous machines and of the whole power system.

Correction to “D-Stability and Delay-Independent Stability of Homogeneous Cooperative Systems” [Dec 2010 2882-2885]

We correct some errors in the statements and proofs presented in Section V of the above mentioned manuscript.