Feasibility of Simultaneous Input-Output Constraints for Tracking in a Class of LTI Systems: Part I

Abstract: This paper addresses the problem of simultaneous satisfaction of input and output constraints for LTI systems with multiple inputs with state feedback and integral action using a Control Barrier Function based governor. Necessary and sufficient conditions for the CBF-based governor to have a feasible solution and for the closed-loop solutions to be bounded and forward-invariant are derived. A systematic design procedure for choosing the free parameters of the CBF-governor is also provided. These free parameters are associated with high-order CBFs, bounds on feasible command signals, and control input magnitude. A companion paper provides several numerical examples to illustrate the results of this paper, especially the feasibility (or infeasibility) of the CBF governor when the conditions are satisfied (or not satisfied).