From static output feedback to structured robust static output feedback: A survey

Abstract

This paper reviews the vast literature on static output feedback design for linear time-invariant systems including classical results and recent developments. In particular, we focus on static output feedback synthesis with performance specifications, structured static output feedback, and robustness. The paper provides a comprehensive review on existing design approaches including iterative linear matrix inequalities heuristics, linear matrix inequalities with rank constraints, methods with decoupled Lyapunov matrices, and non-Lyapunov-based approaches. We describe the main difficulties of dealing with static output feedback design and summarize the main features, advantages, and limitations of existing design methods.

On the noncollocated control of structures with optimal static output feedback: Initial conditions dependence, sensors placement, and sensitivity analysis

“…Despite simplification of hardware, this technique posed some theoretical challenges: The optimization problem is nonconvex, the optimal gain is dependent on system initial conditions, and the existence of a stabilizing static output gain is an open problem in control theory. 24 This control technique was applied in vibration control problems, considering some approaches to the mentioned challenges. Lim et al 25 considered the application of OSOF control with collocated sensors and actuators to reduce vibration and noise of a clamped plate.…”

L1 synthesis of a static output controller for positive systems by LMI iteration

“…Bilinear matrix inequalities can be treated as LMIs by alternately freezing the variables, and LMIs can be efficiently solved numerically. This provides a heuristic algorithm, and such iterative LMI heuristics were gathered in the work of Sadabadi and Peaucelle . The algorithms are easy to implement using the semidefinite programming software tools, and they have monotonically nonincreasing criteria during iterations.…”

“…This provides a heuristic algorithm, and such iterative LMI heuristics were gathered in the work of Sadabadi and Peaucelle. 14 The algorithms are easy to implement using the semidefinite programming software tools, and they have monotonically nonincreasing criteria during iterations. The PK iteration is the simplest one, but it does not always satisfactorily converge to a local minimum.…”

An iterative LMI approach to controller design and measurement selection in self-optimizing control

“…Therefore, it might be better to recast it as an optimization problem for finding, e.g., the H 2 optimal static output feedback (SOF) controller. Contrary to full state-feedback or full-order controllers, which can be solved using Linear Matrix Inequalities (LMI), structured static output feedback generally results in Bilinear Matrix Inequalities (BMI) and remains an open problem [12], [13]. They are often solved to a local optimum by iteratively fixing some variables and solving the resulting LMI.…”