Multi-Stage and Multi-Time Scale Feedback Control of Linear Systems with Applications to Fuel Cells pp 97-108 | Cite as

# Three-Stage Discrete-Time Feedback Controller Design

## Abstract

In this chapter, the results of two-stage feedback discrete-time controller design from Chap. 3 are extended to the three-stage feedback controller design of discrete-time, time-invariant, linear systems. In the case of a general discrete-time time-invariant linear system, the three-stage feedback controller design derivations practically parallel the derivations done for continuous-time, time-invariant, linear systems with the difference equations replacing the differential equations and arrive at the same sets of the three nonlinear algebraic equations and the three linear Sylvester algebraic equations. Those equations have to be solved in order to facilitate the considered three-stage feedback controller design. Consequently, assuming that the solutions of the corresponding linear and nonlinear algebraic equations are obtained, all good features of the three-stage feedback controller designed outlined for continuous-time linear systems in Chap. 4 hold in the case of discrete-time linear, time-invariant, systems presented in this chapter.

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