We consider the problem of finding optimal, robust stabilization of linear systems within a family of nonlinear feedback laws. Investigation of the efficiency of full-state and partial-state based so called NPID feedback schemes proposed for stabilization of systems in robotics applications has provided the motivation for our work. We prove that for a given quadratic Lyapunov function and a giv...

This paper discusses the problem of stability and stabilization of discrete time switched systems, focusing on the design of a robust state feedback control, and a robust static output feedback control. The results are derived using the direct Lyapunov approach and the poly-quadratic function concept. The stabilization conditions are written through linear matrix inequalities relations. The pol...

Stability analysis of polynomial differential equations is a central topic in nonlinear dynamics and control which in recent years has undergone major algorithmic developments due to advances in optimization theory. Notably, the last decade has seen a widespread interest in the use of sum of squares (sos) based semidefinite programs that can automatically find polynomial Lyapunov functions and ...

We show how piecewise quadratic Lyapunov functions can be used to estimate regions of attraction for linear systems with saturation. The central issues of how to restrict the analysis region and how to optimize the size of the domain of attraction are addressed, and the approach is demonstrated on several examples. We observe that the piecewise quadratic Lyapunov functions yield significant imp...

In this paper we present various algorithms both for stability analysis and state-feedback design for discrete-time piecewise affine systems. As in [13], our approach hinges on the use of piecewise quadratic Lyapunov functions that can be computed as the solution of a set of linear matrix inequalities. We show that the continuity of the Lyapunov function is not required in the discrete-time cas...

This paper studies robust local synchronization in multi-agent systems with time-varying parametric uncertainties constrained in a polytope. In contrast to existing methods with non-convex conditions via using quadratic Lyapunov function (QLF), a new criteria is proposed based on using homogeneous polynomial Lyapunov functions (HPLFs) where the original system is suitably approximated by an unc...

An optimization based method is proposed in this paper for the computation of Lyapunov functions and regions of attractions for nonlinear systems containing polynomial and rational terms. The Lyapunov function is given in a special quadratic form, and the negativity of its derivative is ensured using appropriate LMI conditions. The conservatism of the solution is reduced by utilizing Finsler’s ...

Purpose – The purpose of this paper is to present the methodology to the robust stability analysis of a vision-based control loop in an uncalibrated environment. The type of uncertainties considered is the parametric uncertainties. The approach adopted in this paper utilizes quadratic Lyapunov function to determine the composite Jacobian matrix and ensures the robust stability using linear matr...

A class of Lyapunov functions is proposed for discrete-time linear systems interconnected with a cone bounded nonlinearity. Using these functions, we propose sufficient conditions for the global stability analysis, in terms of linear matrix inequalities (LMI), only taking the bounded sector condition into account. Unlike frameworks based on the Lur’e-type function, the additional assumptions ab...

in this paper, sufficient conditions are proposed to investigate the robust stability of arbitrary switched linear systems with uncertain parameters belongs to the known intervals. in addition, a method is then established to determine the maximum intervals of parameters' variations which guarantee robust exponential stability of uncertain switched linear systems under arbitrary switching. in t...