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This paper mainly concerns the issue of asynchronously switched control for a class of continuous-time switched linear systems with persistent dwell time (PDT). Asynchronous switching implies that when a subsystem switches the matched controller remains active for a finite period of time, such that the Lyapunov-like function increases. A semi-time-dependent (STD) multiple Lyapunov-like function with...
In the present paper a bank of local linear observers is designed for an alcoholic fermentation process. The design is based on the respective linear approximants of the mathematical description of the nonlinear process at particular operating points. The target and tolerance operating areas of the process are determined. A residual of the performance of the observers is introduced. A switching mechanism...
The paper deals with the problem of reducing the order of an original high-order asymptotically stable linear switching system by independently approximating the (stable) LTI systems corresponding to every fixed value of the switching signal. Precisely, each reduced-order model is obtained by minimising the L2 norm of a weighted equation error by means of an efficient algorithm that ensures model...
In this note, we investigate the problem of bounded-input bounded-output (BIBO) stability for continuous-time switched linear systems under arbitrary switching. We show that BIBO stability is equivalent to exponential stability under mild assumptions, which is an extension of the well-known relationship between external and internal stability for linear systems.
The paper deals with singularly perturbed hybrid systems. It proposes a methodology for building a graph defining all the rules that ensure the origin is a stable equilibrium in presence of a dwell-time of order of the parameter defining the ratio between the two time-scales of the system. In this framework one can also treat the corresponding problem for interesting particular cases such as: singularly...
This paper focuses on the output-feedback controller design problem for a kind of continuous-time switched linear systems. The switching rule is state-dependent and satisfies a relaxed min-switching logic. The switching rule and the switching output-feedback controller can be derived by utilizing the modified Lyapunov-Metzler inequalities and the obtained closed-loop system guarantees a prespecified...
This paper is focused on stability analysis for a class of time-varying positive linear systems with delays. Two kind of time-varying delays are taken into consideration. One is the time-varying state delay that can be unbounded. The other is the bounded distributed delay. By using a new method, a state-delay-independent and distribute-delay-dependent criterion for asymptotic stability of the system...
This paper investigates the stabilizability of linear impulsive systems. The fact that some linear impulsive systems may be asymptotically stabilizable even though they are not stable under any consistent impulsive law is indicated by a numerical example. A sufficient condition for the asymptotical stabilizability of linear impulsive systems is presented and then the state-dependent impulsive law...
This paper is concerned with stochastic finite-time boundedness analysis and stochastic finite-time state-feedback controller design for discrete-time positive Markov jump linear systems. First, the stochastic finite-time bound-edness of the positive Markov jump linear system is proved to be equivalent to the finite-time boundedness of a relevant deterministic positive linear system. Then a sufficient...
This paper investigates the stability and L2-gain problems for a class of continuous-time periodic piecewise linear systems with possibly non-Hurwitz subsystems. First, the exponential stability of periodic piecewise systems is studied by allowing the Lyapunov function to possibly non-monotonically decreasing over a period. A sufficient condition is established in terms of matrix inequalities. In...
In this paper, the stability problem for a class of discrete-time switched linear systems with bounded additive disturbance is investigated. The disturbance is assumed to be amplitude-bounded and the switching signal is considered to be persistent dwell-time (PDT) switching. The global uniform stability criterion (GUAS) for the nominal switched systems with PDT switching is first established, then...
This paper investigates a new optimal control stabilization for continuous switched linear systems under arbitrary switching. In fact, based on the aggregation techniques and the application of the Borne-Gentina stability criterion. New stabilization conditions under arbitrary switching are deduced. These results issued from vector norms correspond to a vector Lyapunov function. Indeed, the switched...
This paper collects a number of recent results on stability and L2 gain of switched linear systems (both deterministic and stochastic) under a dwell time constraint. The switching signal orchestrates the commutations between linear systems (in the deterministic case) or Markov jump linear systems (in the stochastic case). In the latter case, the switching affects both the dynamics of the underlying...
This paper deals with the stability of a class of Markov Jump Linear Systems characterized by piecewise-constant transition rates and system dynamics. These systems are called Switching Markov Jump Linear Systems. Mean square stability analysis is carried out by studying the time evolution of the second-order moment of the state. A sufficient condition guaranteeing mean square stability under constraints...
In this paper we study the mean stability of continuous-time semi-Markov jump linear positive systems, which are switched linear systems such that their state variables are in positive orthants and their switching signal is a Markov renewal process. The main result of this paper shows that the mean stability is determined by the spectral radius of a matrix. In the proof we utilize a stability-preserving...
For a class of 3rd-order switched linear systems, we explore a way to approximate the spectral abscissa by means of generalized coordinate transformations. Base on the classic result of matrix equation, the minimum of matrix set measure can be obtained after each transformation. By applying transformations iteratively, a computational procedure is developed for finding the transformation matrix and...
This paper investigates globally asymptotical stability issues of two-dimensional linear time-invariant (LTI) switched systems with saddle points. Without resort to any general stability analyzing techniques or ideas based on any type of Lyapunov functions, this paper proposes a globally asymptotical stability (GAS) criterion for such kind of switched systems under arbitrary periodical/quasi-periodical...
In the present paper a new stability analysis and stabilization of continuous-time uncertain switched linear systems is considered. This approach is based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. The stability conditions issued from vector norms correspond to a vector Lyapunov function. Indeed, the switched system to be...
This paper presents a method to compute an epsilon-optimal solution of the control problem of switched linear systems. A difficulty that emerges in the evalution of the optimal solution is that the cardinality of the solution set increases exponentially as long as the time-horizon increases linearly, which turns the problemintractable when the horizon is sufficiently large. We propose a numerical...
Discrete-time Markov jump linear systems (MJLS) and switched linear systems (SLS) stability, ℋ2 and ℋ∞ performance conditions are very similar. Starting from the fact that MJLS second moment stability can be checked through four different linear matrix inequalities (LMIs), we show how one LMI condition can be obtained from the other. Then, we show the stability of SLS may also be checked through equivalent...
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