Dilated Matrix Inequalities for Control Design in Systems with Actuator Constraint

TL;DR

This paper introduces a novel form of dilated matrix inequalities that improve control design for systems with actuator constraints by enabling multi-objective and robust synthesis with tighter bounds.

Contribution

The paper develops new dilated matrix inequalities that separate system and Lyapunov matrices, enhancing controller synthesis for constrained systems.

Findings

Achieves lower $L_2$ gain bounds compared to conventional methods.

Enables multi-objective and robust control design with flexible Lyapunov matrices.

Demonstrates improved performance in systems with actuator constraints.

Abstract

In this paper, we present a new variation of dilated matrix inequalities (MIs) for Bounded Real MI, invariant set MI and constraint MI, for both state and output feedback synthesis problems. In these dilated MIs, system matrices are separated from Lyapunov matrices to allow the use of different Lyapunov matrices in multi-objective and robust problems. To demonstrate the benefit of these new dilated MIs over conventional ones, they are used in solving controller synthesis problem for systems with bounded actuator in disturbance attenuation. It is shown that for the resulting multi-objective saturation problem, the new form of dilated MIs achieves an upper bound for $L_2$ gain that is less than or equal to the upper bound estimate achieved by conventional method.