Exponential Stabilizability of Switched Systems with Polytopic Uncertainties

The exponential stabilizability of switched nonlinear systems with polytopic uncertainties is explored by employing the methods of nonsmooth analysis and the minimum quadratic Lyapunov function. The switchings among subsystems are dependent on the directional derivative along the vertex directions of subsystems. In particular, a sufficient condition for exponential stabilizability of the switched nonlinear systems is established considering the sliding modes and the directional derivatives along sliding modes. Furthermore, the matrix conditions of exponential stabilizability are derived for the case of switched linear system and the numerical example is given to show the validity of the synthesis results

Stabilizability Analysis of Multiple Model Control with Probabilistic: Stabilizability Analysis of Multiple Model Control with Probabilistic

In this paper, we derive some useful necessary conditions for stabilizability of multiple model control using a bank of stabilizing state feedback controllers. The outputs of this set are weighted by their probabilities as a soft switching system and together fed back to the plant. We study quadratic stabilizability of this closed loop soft switching system for both continuous and discrete-time hybrid system. For the continuous-time hybrid system, a bound on sum of eigenvalues of  is found when their derivatives of Lyapunov functions are upper bounded.  For discrete-time hybrid system, a new stabilizability condition of soft switching signals is presented

Ensuring the Stability of Power Systems Against Dynamic Load Altering Attacks: A Robust Control Scheme Using Energy Storage Systems

This paper presents a robust protection scheme to protect the power transmission network against a class of feedback-based attacks referred in the literature as "Dynamic Load Altering Attacks" (D-LAAs). The proposed scheme envisages the usage of Energy Storage Systems (ESSs) to avoid the destabilising effects that a malicious state feedback has on the power network generators. The methodologies utilised are based on results from polytopic uncertain systems, invariance theory and Lyapunov arguments. Numerical simulations on a test scenario validate the proposed approach

Stabilization of markovian systems via probability rate synthesis and output feedback

This technical note is concerned with the stabilization problem of Markovian jump linear systems via designing switching probability rate matrices and static output-feedback gains. A novel necessary and sufficient condition is established to characterize the switching probability rate matrices that guarantee the mean square stability of Markovian jump linear systems. Based on this, a necessary and sufficient condition is provided for the existence of desired controller gains and probability rate matrices. Extensions to the polytopic uncertain case are also provided. All the conditions are formulated in terms of linear matrix inequalities with some equality constraints, which can be solved by two modified cone complementarity linearization algorithms. Examples are given to show the effectiveness of the proposed method. © 2010 IEEE.published_or_final_versio

On Switched Control Design of Linear Time-Invariant Systems with Polytopic Uncertainties

This paper proposes a new switched control design method for some classes of linear time-invariant systems with polytopic uncertainties. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology offers less conservative alternative than the well-known controller for uncertain systems with only one state feedback gain. The control design of a magnetic levitator illustrates the procedure

Linear quadratic regulation of polytopic time-inhomogeneous Markov jump linear systems (extended version)

In most real cases transition probabilities between operational modes of Markov jump linear systems cannot be computed exactly and are time-varying. We take into account this aspect by considering Markov jump linear systems where the underlying Markov chain is polytopic and time-inhomogeneous, i.e. its transition probability matrix is varying over time, with variations that are arbitrary within a polytopic set of stochastic matrices. We address and solve for this class of systems the infinite-horizon optimal control problem. In particular, we show that the optimal controller can be obtained from a set of coupled algebraic Riccati equations, and that for mean square stabilizable systems the optimal finite-horizon cost corresponding to the solution to a parsimonious set of coupled difference Riccati equations converges exponentially fast to the optimal infinite-horizon cost related to the set of coupled algebraic Riccati equations. All the presented concepts are illustrated on a numerical example showing the efficiency of the provided solution.Comment: Extended version of the paper accepted for the presentation at the European Control Conference (ECC 2019

Robust Stability Analysis of Nonlinear Hybrid Systems

We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems

On feedback stabilization of linear switched systems via switching signal control

Motivated by recent applications in control theory, we study the feedback stabilizability of switched systems, where one is allowed to chose the switching signal as a function of $x(t)$ in order to stabilize the system. We propose new algorithms and analyze several mathematical features of the problem which were unnoticed up to now, to our knowledge. We prove complexity results, (in-)equivalence between various notions of stabilizability, existence of Lyapunov functions, and provide a case study for a paradigmatic example introduced by Stanford and Urbano.Comment: 19 pages, 3 figure

Static output-feedback stabilization of discrete-time Markovian jump linear systems: a system augmentation approach

This paper studies the static output-feedback (SOF) stabilization problem for discrete-time Markovian jump systems from a novel perspective. The closed-loop system is represented in a system augmentation form, in which input and gain-output matrices are separated. By virtue of the system augmentation, a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities, which possess a monotonic structure for a linearized computation, and a convergent iteration algorithm is given to solve such inequalities. In addition, a special property of the feasible solutions enables one to further improve the solvability via a simple D-K type optimization on the initial values. An extension to mode-independent SOF stabilization is provided as well. Compared with some existing approaches to SOF synthesis, the proposed one has several advantages that make it specific for Markovian jump systems. The effectiveness and merit of the theoretical results are shown through some numerical example