Variance is Expectation of squared deviation from the mean. Hence  can not be negative in that sense. Standard deviation which is square root of variance is denoted with a + or - prefix. Since it is square root it can be positive as well as negative at the same time.  But covariance and correlation can be negative.  

Thank you sir

Yes, total variation of controller output can be positive or negative. It also depend on your final control element saturation limits or constraints.