LMIs in Control/Click here to continue/LMIs in system and stability Theory/Discrete-Time Transient Impulse Response Bound

The System For the single-input multi-output discrete-time LTI system with state-space realization, where , and and it is assumed that is invertible. It is also considered that be the unit impulse response of the system. The Data , and The LMI If the Euclidean norm of the impulse response satisfies. and if there exist and ,where P > 0, such that Proof The proof follows same procedure as for transient output bound for Discrete time autonomous LTI systems,but taking as the initial condition, so that the unit impulse response matching the free response . This yields the result. Using the non-strict Schur complement, the matrix inequality is equivalent to the inequality .Substituting this and into .gives the desired result. Conclusion This LMI can be used to analyze the Discrete-Time Transient Impulse Response Bound for the given system Implementation This LMI can be used in a problem and can be solved using the solvers like Yalmip,sedumi,gurobi etc,. Return to Main Page: