This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equiv...This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equivalent one-dimensional equation. Further Fuller’s idea is applied on the equivalent one-dimensional characteristics equation. Then using the co-efficient of the characteristics equation, the routh table is formed to ascertain the aperiodic stability of the given two-dimensional linear discrete system. The illustrations were presented to show the applicability of the proposed technique.展开更多
This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an e...This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.展开更多
The effectiveness of this paper lies in the influence of the discretization step on the asymptotic stability of the positive two-dimensional fractional linear systems.It aims at investigating whether,how and when this...The effectiveness of this paper lies in the influence of the discretization step on the asymptotic stability of the positive two-dimensional fractional linear systems.It aims at investigating whether,how and when this step affects the asymptotically stable two-dimensional positive fractional linear continuous-discrete systems.To accomplish this study,a new test was outlined and used so that the asymptotic stability of the system was measured both before and after being exposed to the sampling step.Furthermore,the conditions of that stability were assessed.As a result,the outcome of the approximation shows that the stability is preserved under a particular set of conditions.On this basis,the newly proposed approach is recommended for testing the intended stability of such systems.A numerical example is tested to show the accuracy and the applicability of the proposed tests.展开更多
文摘This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equivalent one-dimensional equation. Further Fuller’s idea is applied on the equivalent one-dimensional characteristics equation. Then using the co-efficient of the characteristics equation, the routh table is formed to ascertain the aperiodic stability of the given two-dimensional linear discrete system. The illustrations were presented to show the applicability of the proposed technique.
文摘This paper proposes a method to ascertain the stability of two dimensional linear time invariant discrete system within the shifted unit circle which is represented by the form of characteristic equation. Further an equivalent single dimensional characteristic equation is formed from the two dimensional characteristic equation then the stability formulation in the left half of Z-plane, where the roots of characteristic equation f(Z) = 0 should lie within the shifted unit circle. The coefficient of the unit shifted characteristic equation is suitably arranged in the form of matrix and the inner determinants are evaluated using proposed Jury’s concept. The proposed stability technique is simple and direct. It reduces the computational cost. An illustrative example shows the applicability of the proposed scheme.
基金funded by the General Directorate for Scientific Research and Technological Development of Algeria(DGRSDT)supported by University of Mostaganem Abdelhamid Ibn Badis(UMAB)initiated by the concerted research project on Control and Systems theory(PRFU Project Code C00L03UN 270120200003)。
文摘The effectiveness of this paper lies in the influence of the discretization step on the asymptotic stability of the positive two-dimensional fractional linear systems.It aims at investigating whether,how and when this step affects the asymptotically stable two-dimensional positive fractional linear continuous-discrete systems.To accomplish this study,a new test was outlined and used so that the asymptotic stability of the system was measured both before and after being exposed to the sampling step.Furthermore,the conditions of that stability were assessed.As a result,the outcome of the approximation shows that the stability is preserved under a particular set of conditions.On this basis,the newly proposed approach is recommended for testing the intended stability of such systems.A numerical example is tested to show the accuracy and the applicability of the proposed tests.
