Improved Approximation for SISO and MIMO Continuous Interval Systems Ensuring Stability

Abstract

In the recent literature, some practical systems have been modeled as interval systems. In this investigation, an improved approximation technique is first proposed for model reduction in single-input-single-output continuous interval systems; then, the proposed technique is extended to reduce multi-input-multi-output continuous interval systems. The proposed technique is based on a multipoint Padé approximation. Additionally, the technique generates a stable model for a given stable system. The results show that the Routh table integrated multipoint Padé approximation is a good way to reduce continuous interval systems.

Appendix A: Interval Arithmetic

The interval operations [20] are defined as

$$\begin{aligned}&[\alpha , \beta ] + [\gamma ,\delta ] = [\alpha + \gamma , \beta + \delta ] \\&[\alpha , \beta ] - [\gamma ,\delta ] = [\alpha - \delta , \beta - \gamma ]; [\alpha , \beta ] - [\alpha , \beta ] = 0 \\&[\alpha , \beta ] \times [\gamma ,\delta ] = [\hbox {min} \{ \alpha \gamma , \alpha \delta , \beta \gamma , \beta \delta \}, \hbox {max} \{ \alpha \gamma , \alpha \delta , \beta \gamma , \beta \delta \}] \\&[\alpha , \beta ] / [\gamma ,\delta ] = [\alpha , \beta ][1/\delta , 1/\gamma ], \gamma \ne 0, \delta \ne 0 \end{aligned}$$