Regional Analysis of Slope-Restricted Lurie Systems

Abstract

This paper considers the stability analysis of nonlinear Lurie type systems where the nonlinearity is both (locally) sector and slope restricted. Convex conditions for verifying stability, computing outer estimates of reachable sets and upper bounds on the induced L 2 gain in a local or global domain are proposed. The conditions use a Lyapunov function that is quadratic on both the states and the nonlinearity and has an integral term on the nonlinearity. Numerical examples outline the benefits of the proposed approach.

Stability analysis of piecewise affine discrete-time systems

“…Thus, following [12, Proposition 2] a unique solution to (7) exists if (I − F 4 ∆) is non-singular for all ∆ ∈ D = {∆ ∈ D n |∆ (i,i) ∈ [0, 1]}. A condition for the wellposedness is then cast as an LMI constraint (see [13], [12]) as in the proposition below.…”

Stability of Sampled-Data Control for Lurie Systems with Slope-Restricted Nonlinearities

“…, m, are necessarily positivedefinite. Note that this form does not require the positivedefiniteness of P , nor the non-negativity of the coefficients λ i (Valmorbida et al, 2018). In this case, the positivitydefiniteness of V should be ensured by other means, as stated in the following lemma.…”

“…In this section, we derive conditions in the form of linear matrix inequalities (LMIs) to assess the asymptotic stability of the sampled-data closed-loop system (1)-(4). The approach is based on the use of looped-functionals (Seuret and Gomes da Silva Jr., 2012) and a generalized Lurietype function (Valmorbida et al, 2018). With this aim, we apply Theorem 1, considering the function V (x) defined in (17) and the functional…”

“…This paper focus on the stability analysis of the sampleddata closed-loop Lurie system. Our approach combines a generalized Lurie function (as Valmorbida et al (2018)) that does not require the positivity-definiteness of the quadratic part nor the positivity of the Lurie-Postnikov coefficients, with a particular looped-functional (similar to the one used in Seuret and Gomes da Silva Jr. (2012) for input saturated systems).…”

A Lyapunov-Lurye Functional Parametrization of Discrete-Time Zames-Falb Multipliers

“…Although the Lyapunov criterion in this letter does not provide lessconservative results than FIR Zames-Falb multipliers, it may be significant to analyze the system purely in the time domain, especially when there is no direct frequency domain description of the system [15]. Moreover, timedomain approaches provide convenience to analyze local stability [16], while an input-output local stability in the frequency domain using Zames-Falb multipliers is given in [17].…”