LMI-based stability tests for LPV and switched discrete-time linear systems through redundant equations

Stability and stabilisability of switched discrete‐time systems based on structured Lyapunov functions

“…In [22, 23], a new method to check stability of switched discrete‐time systems based on a generic augmented state vector to construct a Lyapunov function has been introduced. The condition presented in the sequel is an extension of [22] making use of switched Lyapunov matrices.…”

“…The numerical complexity is associated with the number of scalar decision variables , and the number of LMI rows . Concerning the stability problem, the methods in [8, 9, 23] provide necessary and sufficient conditions, as in Theorem 2 and Theorem 3. These methods are semi‐decidable and depend on a parameter that must be fixed, M in [8, 9], in [23] and N in the proposed technique.…”

“…Concerning the stability problem, the methods in [8, 9, 23] provide necessary and sufficient conditions, as in Theorem 2 and Theorem 3. These methods are semi‐decidable and depend on a parameter that must be fixed, M in [8, 9], in [23] and N in the proposed technique. It is not possible to determine whether the proposed methods always provide better results.…”

“…The second stability condition is based on the existence of a Lyapunov function with an augmented state vector. Structured Lyapunov functions of this form have also been discussed in [18–21] concerned with stability and robust performance for LTI discrete‐time uncertain systems and in [22, 23] for switched systems. Although there are already necessary and sufficient conditions to deal with the stability problem for discrete‐time systems under arbitrary switching, there is room for more efficient methods.…”

Estabilização Poliquadrática Local de Sistemas Sujeitos a Atuadores Saturantes

“…Nesta seção, ilustra-se a contribuição proposta no presente trabalho. São investigados dois exemplos numéricos, o primeiro extraído de (Bertolin et al, 2018) e o outro adaptado de (Oliveira et al, 2009), onde inicialmente o objetivo era verificar a estabilização sem restrições de amplitude nos atuadores. Nos exemplos que seguem, a menos que explicitamente mencionado, foi considerado o limite de saturação simétrico ρ = 1.…”