Linear matrix inequalities for dissipative constraints in stabilization with relaxed non-monotonic Lyapunov function

The state feedback design with a relaxed non-monotonic Lyapunov function in the discrete-time domain is developed in this work. Linear matrix inequalities are derived from both dissipation-based constraint and dissipation inequality for the closed-loop system. The dissipation-based constraint facilitates the stabilization with ΔVk  0 and decreasing (not necessarily monotoincally), instead of ΔVk < 0 along the trajectory. Time-invariant matrix inequalities are derived for linear time-invariant systems. State-dependent matrix inequalities are employed in the derivation for nonlinear input-affine systems.