BALANCING FOR DISCRETE PERIODIC NONLINEAR SYSTEMS

摘要

This paper extends earlier work on balanced realizations for smooth nonlinear systems The main idea behind the global balanced structure, if it exists, is that the linearized system along a nominal solution is balanced in the usual linear time-varying sense. Hence the global nonlinear balanced system is defined as the one that closes the commutative diagram between linearization and balancing. It was shown earlier that such a global balanced realization may not exist in dimensions larger than one (or, if one relaxes the notion of balancedness to uncorrelatedness, in dimensions larger than two.) In this paper, it is shown that by focusing on the orbit points, balancedness or uncorrelatedness can be obtained via interpolation. Extensions for chain recurrent systems are given.