We describe and evaluate a novel approach to formally verify whether a digital control system meets specifications related to step response parameters. In particular, we obtain a state feedback controller designed for a system represented by a state-space model. Then, we analyze whether its required specifications regarding settling time and maximum overshoot are met, using both open-and closed-loop forms and considering finite-word-length (FWL) effects for the latter. We developed our verification approaches inside DSVerifier, which is a verification tool that employs bounded (and unbounded) model checking based on satisfiability modulo theories. Thus, DSVerifier checks performance requirements of digital control systems considering fragility, such as round-off and numerical quantization errors. Our approaches were also evaluated over a set of standard control-system benchmarks extracted from the control literature. Experimental results show that DSVerifier can check settling time and overshoot in control systems suffering from FWL effects, while other existing approaches routinely ignore those issues. Keywords Formal verification • Digital control systems • Finite word length • Controller fragility 1 Introduction A digital control system consists of sensors, controlled systems, control algorithms, and actuators, which together seek to maintain the behavior of a plant's (controlled system) variables under control, i.e., they ensure the desired transientand steady-state responses (Franklin et al. 1998). The development of digital controllers is a crucial task in control engineering since they are routinely used for many different applications, which range from industrial plants to smart cities.