Projection Approach for Interval Systems Approximation: An Extension to MIMO Systems

Abstract

Interval systems are a class of dynamic processes devoted to robotics, computer science, estimation and observer theories, and control engineering. In control applications, the main advantages of intervals are the guarantee aspect and the ease to bound the uncertain parameters. However when the number of uncertain parameters increase, the modeling step become fastidious. One way to reduce complexity in modelling, analysis and control is model reduction. In this brief, an extension of a robust model reduction technique based on singular value decomposition is considered. For a given original interval system represented in the state space representation, an algorithm has been developed, to obtain a new lower order system. It combines the orthogonal decomposition, the balanced technique and the interval arithmetic theory. By testing the Kharitonov’s theorem, the proposed algorithm computes a reduced model that is always robustly stable and present a very low approximation error when comparing with models of existing works. Two examples are presented to illustrate the effectiveness of the proposed algorithm. Its ease of extending to MIMO interval systems without any constraints, and the lowest value of the mean square error (MSE) permit to conclude to its robustness.