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In this paper, the issues of finite-time extended dissipative analysis and non-fragile control are investigated for a class of uncertain discrete time switched linear systems. Based on average dwell-time approach, sufficient conditions for the finite-time boundedness and finite-time extended dissipative performance of the considered systems are proposed by solving some linear matrix inequalities, where using the concept of extended dissipative, we can solve the H∞, L2?L∞, Passivity and (Q, S, R)-dissipativity performance in a unified framework. Furthermore, two form of non-fragile state feedback controllers are designed to guarantee that the closed-loop systems satisfy the finite-time extended dissipative performance. Finally, simulation example is given to show the efficiency of the proposed methods.  相似文献   

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In this paper, methods for improved design of digital tracking controller for a pilot-scale unmanned helicopter are considered. By discretizing the linearized helicopter model, the linear quadratic with integral (LQI) capability is investigated and applied in order to develop an efficient tracking system including a state-feedback plus integral action. The helicopter velocities are used to formulate a prescribed position reference tracking trajectory. When both process and measurement noises are present, a Kalman filter (KF) is combined with the LQI to form a linear quadratic Gaussian with integral (LQGI) tracking system. Simulation studies illuminate both the capability of the controller design and the accuracy of the estimator. Next, H2, H∞ and mixed H2/H∞ controls are designed and the results between methods are produced and compared.  相似文献   

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The present work proposes a relaxed gradient based iterative (RGI) algorithm to find the solutions of coupled Sylvester matrix equations AX+YB=C,DX+YE=F. It is proved that the proposed iterative method can obtain the solutions of the coupled Sylvester matrix equations for any initial matrices X0 and Y0. Next the RGI algorithm is extended to the generalized coupled Sylvester matrix equations of the form Ai1X1Bi1+Ai2X2Bi2+?+AipXpBip=Ci,(i=1,2,…,p). Then, we compare their convergence rate and find RGI is faster than GI, which has maximum convergence rate, under an appropriative positive number ω and the same convergence factor µ1 and µ2. Finally, a numerical example is included to demonstrate that the introduced iterative algorithm is more efficient than the gradient based iterative (GI) algorithm of (Ding and Chen 2006) in speed, elapsed time and iterative steps.  相似文献   

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Given any finite family of real d-by-d nonsingular matrices {S1,…,Sl}, by extending the well-known Li–Yorke chaos of a deterministic nonlinear dynamical system to a discrete-time linear inclusion or hybrid or switched system:
xn∈{Skxn?1;1≤k≤l},x0∈Rdandn≥1,
we study the chaotic dynamics of the state trajectory (xn(x0, σ))n ≥ 1 with initial state x0∈Rd, governed by a switching law σ:N→{1,…,l}. Two sufficient conditions are given so that for a “large” set of switching laws σ, there exhibits the scrambled dynamics as follows: for all x0,y0∈Rd,x0≠y0,
lim infn→+∞∥xn(x0,σ)?xn(y0,σ)∥=0andlim supn→+∞∥xn(x0,σ)?xn(y0,σ)∥=∞.
This implies that there coexist positive, zero and negative Lyapunov exponents and that the trajectories (xn(x0, σ))n ≥ 1 are extremely sensitive to the initial states x0∈Rd. We also show that a periodically stable linear inclusion system, which may be product unbounded, does not exhibit any such chaotic behavior. An explicit simple example shows the discontinuity of Lyapunov exponents with respect to the switching laws.  相似文献   

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This paper illustrates the derivation of a linear parameter varying (LPV) model approximation of a turbocharged Spark-Ignition (SI) automotive engine and its usage in designing a model-based fault detection and isolation (FDI) scheme. The LPV approximation is derived from a detailed nonlinear mathematical model of the engine on the basis of the well known Jacobian approach. The resulting LPV representation is then exploited for synthesizing a bank of LPV-FDI H∞/H? Luenberger observers. Each observer is in charge of detecting a particular class of fault and is designed for having low sensitivity to all other exogenous inputs so as to allow an effective fault isolation. The adopted FDI scheme is gain-scheduled and exploits a set of engine variables, assumed to be measurable on-line, as a scheduling parameters. The goodness of the LPV approximation of the engine model and the effectiveness of the LPV-FDI architecture are demonstrated by several numerical simulations.  相似文献   

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This article deals with the exponential stabilization problems of Takagi–Sugeno (T–S) fuzzy system under aperiodic sampling. The objective is to solve the H∞, L2?L∞, passive and dissipative stability and stabilization problems based on a unified performance index-extended dissipativity. Some new stability conditions consisting of both exponential stability and extended dissipativity criterion are first established. A sampling period dependent Lyapunov–Krasovskii function together with a novel efficient integral inequality, which has the advantage of reducing conservativeness, is adopted. On the basis of the stability conditions, a sampled-data controller that can not only exponentially stabilize the system but also guarantee the prescribed extended-dissipativity performance is then designed. Moreover, an exponential decay rate can be set in advance to achieve better system performance. Finally, a quarter-vehicle active suspension system with considering payload uncertainties and aperiodic sampling is provided for evaluating the validity and superiority of the extended dissipative control approach proposed in this article.  相似文献   

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This paper considers the sampled-data distributed H∞ control problem for 1-D semilinear transport reaction equations with external disturbances. It is assumed that a finite number of point spatial state measurements are available. A Razumikhin-type approach is developed for stability and L2-gain analysis of the closed-loop system. In contrast to Halanay?s inequality based approach, the proposed Razumikhin-type approach not only provides a subtle decay estimate of the selected Lyapunov functional, but also guarantees the H∞ performance index to be negative if certain conditions are satisfied. By introducing a time-dependent Lyapunov functional combined with the use of Wirtinger?s inequality, sufficient conditions for the internal exponential stability and finite L2-gain are derived in terms of linear matrix inequalities. The obtained conditions establish a quantitative relation among the upper bounds on the spatial sampling intervals and the time sampling intervals, and L2-gain. Two numerical examples are provided to illustrate the usefulness of the proposed theoretical results.  相似文献   

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In the work, the finite-time non-fragile l2?l∞ control problem for jumping stochastic systems with input constraints is addressed. An event-triggered mechanism is introduced to reduce the burden of the data communications. Our goal is to design a controller which makes sure that the underlying closed-loop system could be stochastically finite-time bounded at a specified level of l2?l∞ performance. By using the finite-time analysis theory, some sufficient conditions are proposed for the existence of such a desired controller. The availability of the developed method is finally explained by an illustrated example.  相似文献   

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Let {Πτ(m, n): m?≥?n?≥?0} be the family of periodic discrete transition matrices generated by bounded valued square matrices Λτ(n), where τ:[0,1,2,?)→Ω is an arbitrary switching signal. We prove that the family {Πτ(m, n): m?≥?n?≥?0} of bounded linear operator is uniformly exponentially stable if and only if the sequence n?∑k=0neiαkΠτ(n,k)w(k):Z+→R is bounded.  相似文献   

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