Control Design for Linear Uncertain Positive Discrete-time Systems

For linear uncertain positive discrete-time systems this paper proposes an extended way to reflect structural system parameter constraints and positiveness in solving the problem of the system quadratic stability. The new design conditions are proposed, exploiting a set of system parameter constraint representation in the form of linear matrix inequalities to guaranty the closed-loop strictly positiveness, while a Lyapunov principle is focused to guaranty the system quadratic stability. Moreover, only time-invariant strictly positive control law gain is used in the feedback loop. Closely connected to the obtained results is the fact that the impact of nonnegative system matrix structures can be successfully implemented. A numerical example is included to assess the feasibility of the technique and its applicability. Copyright (C) 2021 The Authors.