Suboptimal Control

Abstract

In this chapter, a problem of suboptimal anisotropy-based state feedback control design for linear discrete-time (LDTI) descriptor systems is solved. The problem may be formulated as follows: to find such control law that the closed-loop system is admissible, and its anisotropic norm is bounded by a given positive value. A similar problem for normal discrete-time systems is solved in [1]. The conditions of anisotropic norm boundedness for descriptor systems, connected with the existence of the solution of GDARE (or LMI) and the special type inequality are given in Sect. . But application of these results to design problems is not a trivial task. There exist a number of papers where suboptimal $\mathscr {H}_\infty \,$-based state feedback control is designed. For example, in [1] necessary and sufficient conditions of such control law existence are formulated in terms of generalized discrete-time algebraic Riccati inequalities (GDARI) with one matrix variable; in [1, 1] conditions are given in terms of strict LMIs. Using the methods of control law design, proposed in the mentioned papers, we solve the suboptimal anisotropy-based control problem for descriptor systems.