Order reduction of continuous-time interval systems using Padé-derived compact search bounds and mountain gazelle optimization

Model order reduction of interval systems is crucial for simplifying comprehension and designing reliable controllers while retaining uncertainty bounds. This study introduces a hybrid order-reduction framework that combines split-merge reformulation, Padé approximation, and the mountain gazelle optimization (MGO) algorithm to develop reduced-order interval models (ROIMs). The interval dynamics are first decomposed into lower- and upper-bound fixed-coefficient systems, and Padé approximation is then used to obtain intermediate reduced-order models that retain key time-moments (TiMts) of the actual system. These Padé-defined models yield the reduced-model denominator and provide a basis for defining compact solution-space bounds for optimization, thereby reducing the number of decision parameters and constraining the randomness in the solution region. A search-region control parameter defines a compact search region centered on the intermediate reduced-model coefficients, and the numerator coefficients are optimized by minimizing the integral square error (ISE) between the step-response trajectories of the actual and reduced models. The framework is tested using an 8th-order interval gas turbine model, a 4th-order Zeta converter model, and a 4th-order single-machine infinite-bus power system. Across all case studies, the proposed framework produces ROIMs with enhanced time- and frequency-domain response matching and significantly lower error indices than those of comparative methods. Statistical analysis underscores the significance of the achieved enhancements, and the sensitivity study indicates that the framework remains robust to ± 50% perturbations in the search-region control parameters. These findings support the effectiveness of the proposed method in the benchmark cases reported.