Stability Of Linear Continuous Systems Research Articles

Stabilization of linear continuous systems with limited information

A relationship between transmitting data rate of communication channel and the state expanding rate of continuous linear system is derived to guarantee that the system is asymptotically stabilizable through networked control.

Robust stabilization of linear continuous systems subjected to time-varying state delay and perturbations

In this paper, we address the robust stabilization problem by a memoryless state feedback of linear continuous systems including state time delay and parametric perturbations. Both time delay and parametric perturbations are time-varying and two classes of highly structured and unstructured perturbations are discussed respectively. By making use of the Lyapunov stability approach associated with norm or matrix measure techniques, a new stabilizability criterion and the corresponding memoryless state feedback control laws that guarantee to stabilize the mentioned system are developed. The main feature of the present schemes is that the proposed stabilizability criterion does not involve any matching conditions. Besides defining a family of allowable memoryless state feedback control laws to stabilize the time-delay systems with any one of the two classes of perturbation, it can also determine feedback controllers to guarantee that the closed-loop system have a specified stability degree. Finally, we give a numerical example and computer simulations to confirm the validity and to demonstrate the applicability of the present schemes.

Asymptotic stablity of linear continuous systems containing uncertain parameters†

In a recent paper by the author, the concept of asymptotic stability was extended to systems containing uncertain parameters and a sufficient condition for asymptotic stability of linear discrete systems containing uncertain parameters was developed. In this paper the results are extended and a sufficient condition for asymptotic stability of linear continuous systems containing time-varying uncertain parameters is developed.

"Inners" approach to some problems of system theory

In this paper a formal definition of of a square matrix is introduced. Also defined are the concepts of positive, negative, null, and nonnull innerwise matrix. Applications of these definitions are shown 1) for the necessary and sufficient conditions for the roots of a real polynomial to be within the unit circle, 2) for the roots of a real polynomial to be distinct and on the real axis, and 3) to be distinct and on the imaginary axis in the complex plane. Conditions on relative stability of linear continuous systems as well as on root distribution within the unit circle are also presented in terms of inners. Furthermore, a theorem establishing the equivalence between positive innerwise matrix and a positive definite symmetric matrix is derived for the case when all the roots of a real polynomial are inside the unit circle. Extension of the inners approach to the general problems of clustering of roots as well as of the root distribution in the complex plane is briefly mentioned. Several examples are presented to elucidate the application of the inners concept to some problems that arise in system theory.