An Output-Feedback Design Approach for Robust Stabilization of Linear Systems With Uncertain Time-Delayed Dynamics in Sensors and Actuators

Abstract

In this paper, we propose a control approach for the robust stabilization of linear time-invariant (LTI) systems with non-negligible sensor and actuator dynamics subject to time-delayed signals. Our proposition is based on obtaining an augmented model that encompasses the plant, sensor, and actuator dynamics and also the time-delay dynamic effect. We make use of the Padé Approximation for modeling the time-delay impact on the feedback loop. Since the actual plant state variables are not available for feedback, the sensor outputs, which represent a subset of the augmented system state variables, are used for composing a static output-feedback control law. The robust controller gains are computed by means of a two-stage strategy based on linear matrix inequalities (LMI). For obtaining less conservative conditions we consider the use of homogeneous-polynomial Lyapunov functions (HPLF)– and other decision variables– of arbitrary degree. In our proposition, we also take into account the inclusion of a minimum decay rate criterion in order to improve closed-loop system transient response. Disturbance rejection is also addressed through extensions to $\mathscr {H}_{2}$ guaranteed cost minimization. The effectiveness of the proposed strategy is attested in the design of a controller for the lateral axis dynamics of an aircraft and other academic examples.

Keywords

• Robust control
• time-delay
• linear time-invariant systems
• static output feedback
• linear matrix inequalities