Applications of a model matching framework in switched systems

In this paper we build on our previous work to consider some applications of a prototypical model matching framework where the various mappings involved are systems that switch arbitrarily among n given linear time-invariant (LTI) systems. The design interest was placed on minimizing the worst case ℓ_∞-induced norm of this model matching system over all possible switchings. It was shown that the model matching problem can be solved via linear programming (LP) with an arbitrary a-priori precision. To illustrate the efficiency of the proposed architecture, we consider herein three related applications: sensitivity minimization of switched systems, linear parameter-varying (LPV) control, and cooperative control of dynamic agents. These applications share a common feature that information switching about the system dynamics results in a switched closed-loop system and thus generate the necessity to address transient system stability and performance optimization. A numerical example is included to demonstrate the difference of achievable performance under different switchings.