Motivated by the need to simultaneously guarantee safety and stability of safety-critical dynamical systems, we construct permissive barrier certificates in this paper that explicitly maximize region where system can be stabilized without violating constraints. An iterative search algorithm is developed for maximum volume certified safe stabilization. The region, which allowed take any arbitrary shape, proved strictly larger than regions generated with Lyapunov sublevel set based methods....

This paper investigates robust consensus for a class of uncertain multi-agent dynamical systems. Specifically, it is supposed that the system described by weighted adjacency matrix whose entries are polynomial functions an vector constrained in semi-algebraic set. For this topology, we provide necessary and sufficient conditions ensuring first-order second-order consensus, both cases positive non-positive matrices. Moreover, show how these can be investigated through convex programming using...

The load-following capabilities of power plants became increasingly important in recent years as a means ensuring reliable operation future systems. In this work, we propose generic approach, based on reachability analysis, to rigorously verify the safety critical components that often pose limitations flexibility conventional perform fast load changes. proposed algorithm makes it possible compute bounds all trajectories for range operating conditions while simultaneously meeting practical...

An essential problem in the coordination of multiple agents is formation control. Significant challenges to theoretical design may arise when multiagent system subject uncertainty. This paper considers robust multitask control for agents, whose communication and measurements are disturbed by uncertain parameters. The objectives include achieving desired configuration, avoiding collisions, preserving connectivity topology. To achieve these objectives, we first provide conditions terms linear...

We propose and implement an algorithm based on reachability analysis to estimate the region of attraction (ROA) equilibrium point for nonlinear systems. The stability is obtained via computation forward reachable sets. compare our results with well-established techniques in this area. In particular, we consider optimization Lyapunov function (LF) sub-level set using sum-of-squares (SOS) decomposition, backward sets a target viscosity solution time-dependant Hamilton-Jacobi-Isaacs (HJI)...

Robust synchronization problem is a key issue in chaotic circuits and nonlinear systems. This paper concerned with robust of polynomial system affected by time-varying uncertainties on topology, i.e., structured uncertain parameters constrained bounded-rate polytope. Via partial contraction analysis, novel conditions, both for exponential asymptotical synchronization, are proposed using parameter-dependent matrices. In addition, system, this introduces new class matrix, homogeneous matrix...

Estimating the domain of attraction (DA) an equilibrium point is a long-standing yet still challenging issue in nonlinear system analysis. The method using sublevel set Lyapunov functions proven to be efficient, but sometimes conservative compared estimate via invariant sets. This paper studies estimation problem DA for autonomous polynomial by invariance principle. main idea sets positive polynomial, which characterizes boundary new type admits condition that derivative non-positive,...

Estimating the Domain of Attraction (DA) non-polynomial systems is a challenging problem. Taylor expansion widely adopted for transforming nonlinear analytic function into polynomial function, but performance not always satisfactory. This paper provides solvable ways estimating DA via Chebyshev approximation. Firstly, approximation without remainder, higher order derivatives Lyapunov functions are used DA, and largest estimate obtained by solving generalized eigenvalue Moreover, with an...

Transient stability analysis is a traditional yet significant topic in power systems. In order to obtain the domain of post-fault equilibrium point, Lyapunov method proven be effective and efficient once function has been found. The main innovation this paper consists use rational functions compute largest estimate Region Attraction (ROA) an point for Firstly, non-polynomial systems are reconstructed uncertain differential algebraic via multi-variate truncated Taylor expansion. An iteration...

An increasingly important issue in the area of uncertain systems is estimation Robust Domain Attraction (RDA). Though this topic great interest, most attention has been paid to RDA for polynomial systems. This paper considers rational and non-polynomial systems, both with parametric uncertainties, which are constrained a semialgebraic set. The main underlying idea reformulate original system an by using truncated Taylor expansion parameterizable remainder functions. A novel way compute...

This paper investigates robust consensus for multi-agent systems with discrete-time dynamics affected by uncertainty. In particular, the considers single and double integrators, where weighted adjacency matrix is a polynomial function of uncertain parameters constrained into semialgebraic set. Firstly, necessary sufficient conditions are provided based on existence Lyapunov polynomially dependent an upper bound degree required achieving necessity provided. Secondly, condition integrator...

This paper studies a control synthesis problem to enlarge the domain of attraction (DA) for non-polynomial systems by using polynomial Lyapunov functions. The basic idea is formulate an uncertain system with parameter ranges obtained form truncated Taylor expansion and parameterizable remainder system. A strategy searching output feedback controller estimating lower bound largest DA proposed via optimization linear matrix inequalities (LMIs). Furthermore, in order check tightness estimated...

This brief studies local and global synchronization in multiagent systems with nonlinear dynamics respect to equilibrium points periodic orbits. For synchronization, a method is proposed based on the transformation of original system into an uncertain polytopic use homogeneous polynomial Lyapunov functions. another search for suitable function. The methods exploit linear matrix inequalities have several advantages. In particular, require solution convex optimization problems. Also, more...

While a number of efficient methods have been proposed for approximating backward reachable sets, no synthesis method via sets has developed estimating and enlarging the region attraction (RA). This paper shows how to use enlarge estimate RA linear discrete-time systems, by using an optimal static feedback controller. Two controller design are provided: first enlarges invariant whose existence is ensured zonotope containment; second provides control input Lyapunov stability quadratic...

This study studies robust local synchronisation in multi‐agent systems with time‐varying parametric uncertainties constrained a polytope. In contrast to the existing methods non‐convex conditions via using quadratic Lyapunov function, new criteria is proposed based on homogeneous polynomial functions where original system suitably approximated by an uncertain polytopic system. Furthermore, corresponding tractable of linear matrix inequalities have been provided exploiting squares...

This paper addresses robust discrete-time consensus problem of multiple agents with uncertain structure, where the network coupling weights are supposed polynomial functions an vector constrained in a semialgebraic set. Based on Lyapunov stability theory, necessary and sufficient condition for is proposed. Then, we investigate positive weighted network, also provided based property matrix. Corresponding conditions derived by solving linear matrix inequality (LMI) built exploiting...

The integration of mixed-critical tasks into a platform is an increasingly important trend in the design real-time systems due to its efficient resource usage. With growing variety activation patterns considered systems, some them capture arbitrary patterns. As consequence, existing scheduling approaches mixed-criticality (MCs), which assume sporadic with implicit deadlines, have sometimes become inapplicable or are ineffective. In this paper, we extend sporadically activated task model...

Estimating the region of attraction for partially unknown nonlinear systems is a challenging issue. In this paper, we propose tractable method to generate an estimated with probability bounds, by searching optimal polynomial barrier function. Chebyshev interpolants, Gaussian processes and sum-of-squares programmings are used in paper. To approximate non-polynomial dynamics, mean function model computed represent exact dynamics based on interpolants. Furthermore, probabilistic conditions...

This paper addresses the estimation of domain attraction for a class hybrid nonlinear systems where state space is partitioned into several regions. Each region described by polynomial inequalities, and one these regions complement union all others in order to ensure complete cover space. The system dynamics defined on each independently from functions. problem computing largest sublevel set Lyapunov function included considered. An approach proposed addressing this based linear matrix...