Absolute Stability of Nonlinear Systems with Piecewise Linear Sector Condition

Robustness Properties of Nonlinear Systems: Absolute Stability of Linear Systems

In this paper we present a new approach to the Popov's Positivity Theorem and new statements and proofs of Absolute Stability Theorems. In the rst chapter we establish connexions between Riccati equations, Kalman-Yakubovitch-Popov systems and Luri e systems. We prove this results for stabilizable and antistabilizable solutions avoiding Youla's factorization. In the second chapter we state the A...

Piecewise Constant Controlled Linear Fuzzy Systems

Exponential Stability of Linear Systems with Multiple Time Delays

In this paper, a class of linear systems with multiple time delays is studied. The problem of exponential stability of time-delay systems has been investigated by using Lyapunov functional method. We will convert the system of multiple time delays into a single time delay system and show that if the old system is stable then the new one is so. Then we investigate the stability of converted new ...

Stability Analysis of Discontinuous Nonlinear Systems via Piecewise Linear Lyapunov Functions

The purpose of this paper is to present a stability analysis of discontinuous nonlinear systems using Piecewise Linear Lyapunov Functions (PWLLFs). The functions are parametrized by hyperplanes, which intersect the stability region, and stability conditions are formulated as Linear Programming Problems (LPs) in terms of the parameters inserted by the hyperplanes. An interesting feature of the a...

Regions of Stability for Limit Cycles of Piecewise Linear Systems

This paper starts by presenting local stability conditions for limit cycles of piecewise linear systems (PLS), based on analyzing the linear part of Poincaré maps. Local stability guarantees the existence of an asymptotically stable neighborhood around the limit cycle. However, tools to characterize such neighborhood do not exist. This work gives conditions in the form of LMIs that guarantee as...