An improved output feedback controller design for linear discrete‐time systems using a matrix decomposition method

Abstract

Summary This paper presents the design of output feedback controllers for discrete‐time (DT) linear systems. New sufficient LMI conditions are derived for designing static H2$$ {H}_2 $$ and H∞$$ {H}_{\infty } $$ controllers using decomposition of an auxiliary matrix. The decomposition facilitates linearization of nonlinear term of reduced size to obtain linear matrix inequality criteria. This leads to less conservative results as shown in the numerical examples. In addition, the proposed static output feedback criteria is also used for designing dynamic output feedback controllers for DT systems. Furthermore, a comparative study is also made for the proposed design method with the results existing in the literature. Finally, a DT static output feedback H∞$$ {H}_{\infty } $$ controller is designed for a quarter‐car suspension system. Simulation results are provided to show the efficacy of the proposed design method.

Modified Riccati iterative algorithms for stochastic coupled algebraic Riccati equations of linear stochastic Markovian jump systems

“…Among these studied problems, the linear quadratic regulator (LQR) problem has attracted a lot of attention in the field of control theory and applied mathematics [13][14][15][16], and its main idea is to design a feedback control law(mostly linear) so that the given quadratic performance index can be optimized, and the LQR problem of linear stochastic systems with Markovian jumps is discussed, see [17][18][19][20][21].…”