Energy functions for dissipativity-based balancing of discrete-time nonlinear systems (Q850841)

The paper presents theory concerning nonlinear discrete-time dissipative systems that establishes input-state-output relations and proposes storage functions used for them in nonlinear balancing. Using some dynamic optimization problems and nonlinear discretization algorithms based on Tayor-Lie series and numerical integration approximations to continuous-time systems such storage functions are found. Also nonlinear discrete-time versions of controllability and observability functions, its properties and algorithms to find them are presented. The theory is well illustrated in the example of an electric motor dynamics.