Applying the Cayley-Hamilton Theorem to Analytic Synthesis of Modal Control by Output for Linear Time Invariant Systems Having the Order Equal to the Product of Inputs and Outputs

A new analytical approach to static output feedback pole placement for linear time-invariant systems having the order equal to the product of inputs and outputs, and controllability and observability indices take the highest and the lowest possible values is proposed. The approach uses the Cayley-Hamilton theorem in relation to a closed-loop control system matrix. The applicability of the proposed method of static output feedback pole placement is not limited only by fourth-order systems with two inputs and two outputs. Besides, the method applicability does not depend on whether the system is reducible to modal control by state with fewer inputs or to modal observation with fewer outputs. On the examples of sixth-order multi-input multioutput systems not reducible to systems with fewer inputs or outputs, the process of obtaining analytical solutions to the problem of modal control by output, providing desirable pole placement is demonstrated. For systems from the considering class, the obtaining solutions are unique.