Observer-Based Robust Controller Design With Simultaneous Optimization of Scaling Matrices

This paper addresses the design problem of robust controllers, which are composed of state observers and state-feedback controllers, for linear time-invariant parameter-dependent (LTIPD) systems. The design problems for continuous-time and discrete-time LTIPD systems are both addressed. The state-space matrices of the LTIPD systems are supposed to be multiaffine with respect to time-invariant parameters, and the supposed uncertainty blocks, which have an ability to define various design requirements, are characterized by scaling matrices, e.g., D- and (D, G)-scaling. We propose a tractable condition for the simultaneous design of robust controllers and scaling matrices via dilated linear matrix inequality technique. A numerical example demonstrates the effectiveness of our method.