3 [7] Consider a state space transition function which is assumed to satisfy the identity, semi-group and causality (i.e. non-anticipative) properties characterizing an input-state system: S: (t1, to, x, u) to ti; to, t R, x X, u EU, where u is a family of input functions of time {u,, s E R} taking values at any instant in the set U, X is the system state space, and where takes values in X. Here X = R" and U = Rm for some m, n. = (i) [1] Assume that u, is given in the instantaneous state feedack form u Mo(s, to, x, u), to s; to, s ER, where M is a matrix mapping from the state space X into the control set U. Does the resulting system function (ti, to, x, u*) possess the state space system identity, semi-group and causality properties? (ii) [2] Answer (i) in case u = Mo(s1, to, x, u*), to s-1 (iii) [2] Answer (i) in case u = Mo(s + 1, to, x, u*), to s+1 (iv) [2] Suppose there is an instantaneous output map y(t)= n(t, (t, to, x, v*), v), to t, taking values in the output value set Y = RP, for some p, for all xEX and v EU. Assume v(n(s, (s, to, x, v*), v)), to s, where is a func- tion mapping the output set Y into the control set U. Does the resulting system function (t1, to, x, v*) possess the state space system identity, semi-group and causality properties