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The paper considers the generalization of the method proposed by I.B. Furtat,P.A. Gushchin in "Automation and Remote Control", 2021, No. 4 for systems withan arbitrary ratio of the number of input and output signals and with aguarantee of their being in a given set. To solve the problem, two coordinatechanges are proposed. The first coordinate change reduces the output variableof the system to a new variable which dimension does not exceed the controldimension. The second coordinate change allows one to pass from a constrainedcontrol problem to an unconstrained one. In order to illustrate the efficiencyof the method, the solution of two problems is considered. The first task isstate feedback control of linear systems, taking into account the constraintson the control signal and phase variables. The second task is output feedbackcontrol of linear systems with a restriction on output and control. In bothproblems, checking the stability of the closed-loop system is formulated interms of the solvability of linear matrix inequalities. The obtained resultsare accompanied by examples of modeling that illustrate the efficiency of theproposed method.

Control of dynamic systems with restrictions on input and output signals