LMIs in Control/pages/LMI for Mixed H2 Hinf Output Feedback Controller

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LMI for Mixed Output Feedback Controller

The mixed output feedback control has been known as an example of a multi-objective optimal control problem. In this problem, the control feedback should respond properly to several specifications. In the controller, the channel is used to improve the robustness of the design while the channel guarantees good performance of the system.

The System[edit | edit source]

We consider the following state-space representation for a linear system:

where , , , and are the state matrix, input matrix, output matrix, and feedforward matrix, respectively.

These are the system (plant) matrices that can be shown as .

The Data[edit | edit source]

We assume that all the four matrices of the plant, , are given.

The Optimization Problem[edit | edit source]

In this problem, we use an LMI to formulate and solve the optimal output-feedback problem to minimize both the <> and <> norms. Giving equal weights to each of the norms, we will have the optimization problem in the following form:

The LMI: LMI for mixed /[edit | edit source]

Mathematical description of the LMI formulation for a mixed / optimal output-feedback problem can be written as follows:

where and are defined as the and norm of the system:

Moreover, , , , , , and are variable matrices with appropriate dimensions that are found after solving the LMIs.

Conclusion:[edit | edit source]

The calculated scalars and are the and norms of the system, respectively. Thus, the norm of mixed / is defined as . The results for each individual norm and norms of the system show that a bigger value of norms are found in comparison with the case they are solved separately.

Implementation[edit | edit source]

A link to Matlab codes for this problem in the Github repository:


Related LMIs[edit | edit source]

External Links[edit | edit source]

  • [1] - LMI in Control Systems Analysis, Design and Applications

Return to Main Page[edit | edit source]

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