Bounded control and discrete-time controllability†

The discrete-time linear system xk+1 = Axk + uk (k = 0, 1,[tdot]), for which the input uk belongs to an arbitrary bounded and convex set Ω, is considered. The error in the sufficiency proof of the controllability result when 0 ∊ ri (Ω) owing to Wing and Desoer is avoided by using convexity arguments, and the result is extended to encompass the case 0 ∉ ri (Ω)