A new design technique for linear continuous-time systems subject to multiple integral and output constraints is proposed to synthesise linear state-feedback control providing a suboptimal value of a performance index being a convolution of integral criteria and maxima in time of norm of linear functions of state and control variables. The technique is based on quadratic Lyapunov functions and linear matrix inequalities (LMIs). The approach is extended to systems with norm-bounded uncertainty. Efficiency of the technique is illustrated by synthesising a suboptimal linear shock isolator.