Stability Margins of MIMO Linear Interval Systems

In this paper, a worst-case margin algorithm is proposed to deal with the stability margins of Multi-Input Multi-Output(MIMO) linear time-invariant interval systems. Firstly, the Kharitonov's Theorem and V. Krishnamurthi's corollary on Routh criterion are used to prove the stability of MIMO linear interval systems with affine parametric uncertainty structure. In particular, it can be used to analyze the stability regions of interval systems with parameters as well Secondly, each eigenvalue function of the MIMO linear interval systems is regarded as a Single-Input Single-Output(SISO) linear time-invariant system. Then the frequency domain approach and optimization algorithms are applied to develop a computationally tractable algorithm for calculating the stability margins. Moreover, this method can be extended to the non-minimum phase system. Finally, the engineer relevance examples are presented to validate the effectiveness and accuracy of the proposed method.