Design of Simple Control Machines

Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

Let $$A(\cdot )\in L^\infty (\mathbb {R}^+; \mathbb {R}^{n\times n})$$ be T-periodic. In the case that $${\upsigma }(\mathscr {P})\subseteq \mathbb {B}$$ (where $$\mathscr {P}$$ is given by ()), we need to do nothing from perspective of the periodic stabilization. If $${\upsigma }(\mathscr {P})\nsubseteq \mathbb {B}$$, we will find a T-periodic control machine $$B(\cdot )\in L^\infty (\mathbb {R}^+; \mathbb {R}^{n\times m})$$ so that $$[A(\cdot ), B(\cdot )]$$ is linear T-periodic feedback stabilizable (LPFS, for short). Among all such control machines , how to choose a simple one? To answer this question, we should first explain what means simple one. From different perspectives of applications, one can give different definitions of simple machines. We will define two kinds of simple control machines and provide the ways to design the corresponding simple control machines . When design them, Theorem  will be used. Throughout this chapter, we focus ourself on those T-periodic $$A(\cdot )$$ with $${\upsigma }(\mathscr {P})\nsubseteq \mathbb {B}$$.

Keywords

Periodic Equations Stabilization Simple Control Machines ODE 